Inverse Functions

[@faithisabel25]

You're such a great teacher :-) Will never survive my precal without your videos. Maraming Salamat (Thank you) :-)

[@profrobbob]

THANKS for your continued support...my videos will be here for you whenever you need them! You might find it easier to search things on my website at www.profrobbob.com

[@TheFuture-ub4du]

I've been enlisted in the military for 3 years so getting back to studying was a little intimidating. I'm back in school now and I owe my current confidence in my precalc class to your videos. I've come to rely upon your videos to give that extra insight and explanation that an hour of class just doesn't offer. Thank you - Chris

[@profrobbob]

You're welcome Chris...and THANK YOU for taking the time to seek out extra help and choose my channel to learn from and subscribe to! I hope I can continue to build your confidence and maybe even "enjoy" math:) Thanks for supporting our country and good luck in wherever the future leads you...Mr Tarrou

[@alyssagranato8959]

What my professor tried to explain in 1 hour and 45 minutes was explained much more easily by you! Love this guy!!

[@fitnesschallenge1000]

Just wanted to say thanks again for your help. I scored a B in my college algebra class, only 3 of 12 passed. I shared your site with them and some were upset and felt they should not have to go beyond the professor to learn. They failed the class. I am responsible for my education and this site was ON TIME!!! Thanks again.

[@profrobbob]

CONGRATULATIONS fitnesschallenge1000 on that B!...and you're welcome. Thanks for taking the time to share your success and for subbing and sharing my channel. Chinese Proverb: "Teachers open the door but you must enter by yourself." Keep that positive, responsible attitude and you can be whatever/where ever your dreams take you...and trust me, you're never too old to dream! (our dream is to someday have a million subscribers just like you:)

[@sluggingbread]

You're the man Prof Rob. Keep shelling these bad boys out. I think I found my long lost love for math again. You are an exceptional instructor. I always look forward to your lessons and please, never forget us!

[@profrobbob]

sluggingbread and please never stop spreading the word and sharing this channel with everyone to help us keep growing and helping others like you find the "love of math" again or for the first time! Thanks for taking the time to share your learning experience and compliments too.

[@profrobbob]

OMGoodness...THANK YOU for those empowering words! And that is exactly what my wife is working on...trying to find new ways to make my channel information available to "everyone" "everywhere" without the need to search through a ton of videos first. If my channel info could be added to new student packet info, to student tutoring info boards, school websites etc...those are the types of places she is starting with. You can start by spreading the word to others and keep supporting:)

[@motherof3at22]

Your awesome. I have learned more from you than both my college math teachers combined. Because of your instruction, I passed my algebra 1 and 2 classes with an A and B. I would recommend you to anyone.

[@profrobbob]

CONGRATS! Thanks for watching and subbing and taking the time to learn from my videos! Sounds like you have been watching for a while too:) I hope you will continue to share my channel with others and help me groW and I look forward to being your KZbin teacher for any of your future math classes!

[@DAVIDSTEPHENS8]

This guy is a teacher's teacher!! He simply exudes a passion for teaching maths. Thank you for your indefatigable efforts.

[@profrobbob]

You're welcome and Thank you David for the compliments…don't forget to support and SUBSCRIBE!

[@jordanperez8055]

We should replace all math teachers with videos of ProfRobBob....

[@profrobbob]

BAM!!!!....I'm all in for getting every math teacher to recommend my videos as an additional study tool for each and every student (as long as they "ALL" SUBSCRIBE, Like, and support the ads on my channel and help me groW...BAM!!! How about if I put you in charge of that at your school Jordan Perez :)

[@jordanperez8055]

You bet!

[@profrobbob]

THANKS Jordan Perez I'll be looking fro a jump in my subscriber count soon:)

[@profrobbob]

Good to see you back for more, and I appreciate being the one you choose to watch and give your valuable self-study time to! Keep up that self-motivation and positive outlook:) And thanks for your continued support and admiration.

[@jacobogle5435]

I wish you were my pre-calculus professor. You have pretty much been the only way I understand this content all semester. Thanks a lot!

[@profrobbob]

You are so welcome Jacob Ogle and THANK YOU for choosing me as your KZbin teacher and for taking the time to share your appreciation with me! Students like you are why I love to teach and work so hard to groW this channel and keep it FREE...thanks for subbing and I hope you are sharing it with all the students and teachers at school!!! Sharing + Subscribing = More students get math help for free...BAM!!! (and #ProfRobBob keeps growing to help others like you:)

[@profrobbob]

You are welcome....and thank yooooooou for picking my channel to learn from:) I vow to "make math FUN" while learning at the same time...thanks for enjoying my teaching style!

[@profrobbob]

You are very welcome. Thank you very much for watching. I hope you do fantastic on your upcoming test!

[@kevinregalado1669]

This Channel truly helps me when I'm confused about a lesson. Thank you so much.

[@michaelfeduccia7989]

You always clear the muddy water for me! I love your videos!

[@amilagayan5223]

I am from Sri Lanka.......now iam in NY,i take pre cal.. class,but i cant understand anything from the class,i just only go and marked attendance. i only learn from your videos,you are a great teacher. i salute you Sir.........God bless you.....

[@profrobbob]

THANKS for sharing your story Amila Gayan and for taking the time to find help on KZbin and choosing Tarrou's Chalk Talk to learn from! Please share my channel with the rest of your class and remind them to support by liking, sharing and SUBSCRIBING!

[@whiteninjaooo]

you must be in my class lol

[@youseffattal2866]

Exactly like my situation ! came from foreign country and taking pre calc. I only go for attendance and to for homework delivery and test. I rely on your videos 100%. We couldn't thank you enough.

[@profrobbob]

You're welcome and Yousef Fattal although I don't condone not going to class I do appreciate that Tarrou's Chalk Talk is your go-to channel for math help...BAM!!!

[@MeggieChristine12345]

I am definitely going to pass my college algebra final now. Thank you SO much!!

[@mynameisnotcory]

you're like a teacher that was supposed to be a comedian, but decided to be entertaining in a helpful way! great video!

[@profrobbob]

I apologize for the delayed reply to such a great comment:( Thanks for appreciating my attempt at humor and sticking around to learn the math! (…if I only made a comedians salary:) I hope you continue to enjoy your learning experience from Tarrou's Chalk Talk and will share my channel with everyone you know looking for math help:D

[@MurrayMelander]

I keep coming back to this video. One of the best if not THE best explanation of the subject I've found so far.

[@profrobbob]

Murray Melander thanks for your continued support! Please keep sharing my channel too:D

[@profrobbob]

You're very welcome...and thank you for your support by liking and subscribing! Now go pass that test with confidence:)

[@fitnesschallenge1000]

This guy totally rocks. I am in a College Algebra class and I have a professor that does not explain anything.... blazes through problems... and goes on to the next. I now find myself checking on my iphone for the topic he is discussing. If I see Professor Rob has a video, I veg out and come home and teach myself with his videos. Bro, you are a life saver. Thank you for putting this site up.

[@profrobbob]

Sounds like you need to share my channel with the rest of your class too fitnesschallenge1000 :D Thanks for choosing Tarrou's Chalk Talk to watch, subscribe to, and learn math from and glad I could provide you with the life ring for that sea of math...lol

[@namratachauhan6386]

Thanks so much for your videos. After school and tuition classes, I get so exhausted that I rarely get any time for self-study. But, your videos are just amazing.. I just start off with my studies even after such a hectic schedule with a lot more enthusiasm. Thanks a lot Professor. You ARE the Best teacher!! I never get bored watching your videos. :)

[@jensgoode8640]

I was waiting for the words of encouragement to go do my home work. You left me hanging Rob! I suppose I will have to be satisfied for the amazing explanation and examples. You helped me get an A in Trig and now you are going to do the same for me in Pre-Cal. Thank you.

[@profrobbob]

Just to save a couple steps of algebra in the process of solving for y. You can distribute the y and ultimately get the same answer:) Thank you very much for watching!

[@profrobbob]

You are very welcome. I am thrilled you are finding my videos so helpful:) I hope you do great in your class! Please help me by spreading the word.

[@profrobbob]

You're welcome…you keep watching, liking, sharing, supporting and SUBSCRIBE… and I'll keep making videos:)

[@pieman1234sanford]

Re-tweet thanks Professor this is the best help i have ever had i have a terrible teacher for alg 2 he just really lazy and does not teach anything so i have to go home and learn it my self thanks again you rock

[@ahmadmohammed6902]

You are by far the best I have seen on youtube. Your teaching skills are amazing the way you explain things is so clear

[@profrobbob]

THANK YOU for the compliments and for choosing my channel to study with and sub to! Spread the word:D

[@profrobbob]

Another Closed Captioned #math lesson

[@dburks10]

Thank you for making these videos. I am a college student taking Algebra for the first time after having been out of school for 25+ years, so needless to say... I have gotten lost in the class room and in the txt book. Your site is one of the youtube sites I have been depending on to help me find my way to better understanding. Thanks for making it not only fun but understandable.

[@hassanibrahim54]

Very smart, great teacher. you are one of the best teacher in social media.

[@profrobbob]

Thanks for supporting and the great compliment! Please keep spreading the word:D

[@georgesadler7830]

Professor RobBob, thank you for explaining the graphic and analytical approach to finding Inverse Functions in Algebra Two/Precalculus.

[@Mr.G626]

thank you for putting together this PreCalculus playlist, it is truly invaluable. i see your channel has grown substantially as you're at 144k subscribers now, that is awesome. again, thank you for all that you do.

[@profrobbob]

You're welcome and thanks for watching...please continue to share this free resource with classmates, friends and teachers as you remind them all to sub and share thru social medias as well, to help us continue to grow and remain free...BAM!!!

[@profrobbob]

Thanks for saying so...I'm glad to see you are still watching, learning, and liking my channel:) Now BAM!!!...go share my channel with others who will benefit:D...and thanks again for the support!!!

[@darrinhartford5268]

You present problems and solutions in a very clear and understandable way. You have been and I'm sure will be a huge help in my college algebra class. If I had you for a teacher I have no doubt I would be a straight A student. Thank you for doing these videos because you make math make sense!

[@profrobbob]

BAM!!! Darrin Hartford Thanks for choosing my channel to watch and learn from! I too have no doubt that with your positive attitude and drive to find outside resources to study with you will be at the top of your class...BAM!!! Thanks for taking time to "thank the teacher" and please continue to help me groW by liking, subbing, supporting the ads, sharing my channel with your friends, class and teachers too:D

[@thomashunt504]

Wow, I never knew that the internet could be used in a purpose this glorious..... Keep up the delicious videos, they help me maintain dominance over all the other kids in my Algebra 2 class. You are literally virtual math teacher in existence.

[@brendaannelovesjesus]

I agree! I'm going to tell everybody at my college! I love the way you teach and your enthusiasm is off the charts!

[@profrobbob]

BAM!!!!...that's what I like to hear:)...thanks again Brenda, my wife and I really appreciate the appreciation and support! We dream someday to see an "M" next to my subscriber count...and you and your sister by doing what your doing gets us one step closer to that dream:) (it's hard to get a math video to go viral...lol)

[@gnarniabmx]

Just wanted to say, you're a boss my friend, keep on mathing

[@profrobbob]

Thanks for choosing Tarrou's Chalk Talk and I hope you "keep on watching!"

[@profrobbob]

To find an inverse function, switch the x & y variables and resolve for y. So you first go to x=sqrt(y), then square both sides so your inverse function is x^2=y. THANKS!

[@oceanranger3819]

nigga stfu

[@profrobbob]

You're WELCOME very much!...and Thanks for choosing my video to learn from too:)

[@birdseed41]

You just saved me at least an hour of trying to decipher my textbook. Thanks! Just subscribed :)

[@profrobbob]

BAM!!! ...and now you'll have more time to study Erin Monk :) Glad to hear I earned a subscriber and I hope you will share your time-saving technique with all your friends, classmates, and teachers! You can even spread the word thru social media...and remind them all to SUBSCRIBE, SUPPORT and SHARE to help these free educational channel continue to groW and remain FREE! Our latest goal is 100,000 subscribers by 2015...so get busy, now that you'll have all this extra time...lol:D

[@powerkoval]

Always the best and straight forward explanations! THANK YOU!

[@profrobbob]

You're welcome Koval Dmitry ! ...thanks for watching too.

[@kristaaagorner]

I had the flu last week and wasn't able to attend class. Your videos are totally saving me! I always watch your videos to accompany my lectures anyway. Thanks so much :)

[@profrobbob]

You are so welcome! Thanks for supporting by watching, liking, subscribing and taking the time to share that with me, I hope you're feeling better & I really appreciate your continued support:D

[@themrjvion]

I wish your channel starts growing faster sooooon. I read your goal was 100,000 for 2015 and you're pretty close! Hopefully you can see that M next to your sub count because you surely surely do deserve it!

[@profrobbob]

Jvion I hope you're right:) Thanks for watching and taking the time to comment...don't forget to like, sub and spread the word to help us keep growing and reach that goal :D

[@profrobbob]

This was one of my early videos that I use to do after school hours from my classroom...must have been a rough day in class:( Glad to hear that you self-motivated yourself to pull off that A! WOW!!!...See what happens when you get help from Prof Rob Bob...lol Thanks for the support of liking and subscribing and I look forward to teaching you and all your friends Pre-Calc!

[@jtorres1800]

The excitement was great at the end! lol 10 years later still making an impact! I should say 12 years lol.

[@profrobbob]

THANKS for choosing my channel to learn from:)

[@strawberrydm1]

Wow I feel so lucky to find your video. You are great as teacher, cant say enough of you!!! Thank you

[@profrobbob]

You're welcome and THANK YOU for choosing #ProfRobBob to learn from Desire Macedo and subscribe to! Please tell all your friends/classmates to watch and do the same:D

[@aliabrahimi3711]

Professor Rob is very concise but includes examples and related subject in one short video. This is very rare. Specially lack of examples in other teachers videos can be very confusing. But not with Professor Rob.

[@profrobbob]

Thanks for the testimonial ali abrahimi! I make my videos like I teach, as full lessons. You will find a lot of my newer videos much longer for that reason but I also try to include time-stamps in the descriptions to allow you to jump to each example. Please remember to Like and SUBSCRIBE to my channel to help me continue to groW and help others!

[@colettewarren7129]

Thank you once again for your explanation a light bulb went off in my head and everything just makes so much more sense. I am currently doing revision for my final exams and I am super excited. since watching your videos I have passed all my tests and I have made DP. That means I qualify to write final exams.

[@profrobbob]

I'm so proud and excited for you Colette Klassen and I'm honored to be a part of your success! Is your niece still doing good too?! Let us know when you are ready to have that meeting, we look forward to meeting you both:) Best of luck with those finals...I know you'll pass them like BAM!!!

[@jeanjaime5494]

ProfRobBob u the best, keep up the good work. God bless you.

[@profrobbob]

Jean Jaime thanks! Don't forget to support, like, subscribe and share with others:D

[@profrobbob]

Every time you solve an equation you use inverse functions whether you adding a number to both sides of an equation to cancel subtraction, use logarithms to solve equations with the variable in the exponent, or use inverse trig functions to find missing angles of a triangle. Math helps to build everything we use everyday. As far as Phi...I have not studied that in a very long time...so I have no comment.

[@mhrmhfathima3342]

I'm studying at GCSE level and I understand these videos simply due to the fact that these videos are brilliantly explained an are f-(mundane)=not boring

[@profrobbob]

Glad to hear you are finding this channel so helpful...thanks for choosing to study and sub with Tarrou's Chalk Talk...BAM!!!

[@SkotiChief]

I'm 100% sure this will help me on my test tonight.. Thank you Prof.

[@benjaminphillips5088]

You're an amazing educator ! Thank you for posting these videos.

[@profrobbob]

THANK YOU Benjamin Phillips and thank you for being an amazing student and studying and watching them...BAM!!!

[@dcristancho02]

Dude! thank you so much I wish my Ph.D professor would explain half as well as you do...so many thank yous, I'm actually understanding this material thanks to you!!

[@samdonahue4328]

Your videos are awesome, I've learned so much in three of them! I plan on watching regularly, it's the only way I'll get through Algebra 2! Thanks so much for posting these videos.

[@profrobbob]

Thanks for choosing my channel and subscribing Sam! Keep up those great study habits and continue to take advantage of more of my videos:)

[@DavidJapanese]

I wish I had this in 2004-2006... You should get an award

[@kentallred7200]

My tuition should be in your bank account.

[@profrobbob]

If only we could work that out!…lol Thank you Kent for supporting my channel by watching, liking, subscribing! The only thing left is SHARING my channel with EVERYONE you know and reminding them to show the same support. The growth of educational channel like mine depend on supportive viewers like you! There is a lot of time and passion put into these "teaching" channels and allowing the ads to run and clicking on them is a way to repay all the teachers who are so giving of their time and passion for teaching. A great gift this year would be to "THANK A TEACHER" as I thank you once again for supporting my efforts:D

[@zhengyangsong]

Thanks for your teaching, your lecture is very good!!!!!!!!!

[@profrobbob]

You're welcome...thanks for watching! Please sub and share too:)

[@bcoll1082]

Excellent as always Mr. Tarrou. Thank you.

[@profrobbob]

You're welcome Brian...thanks for the continued support!

[@profrobbob]

By the time you see this I hope you will have passed your test with that 100% that you deserve for seeking out the extra help!...you're welcome and thanks for liking, and please share my channel with others who may benefit as well:D

[@yuliangonzalez4898]

I go to school the teacher goes over the lesson, i leave lost always. Thank you, if it wast for you i would have failed a long time ago. You keep me engaged and is only a video, my math teacher puts me to sleep.

[@profrobbob]

+gonzlez julian Nice to hear that you are enjoying my videos and are taking the time to find the help you need yourself...those study habits will always be beneficial! Sounds like you should tell the rest of your class to watch, like and sub to this channel too:D...BAM!!!

[@profrobbob]

I can't put a link in the comment area but you can search my channel for First Fundamental Theorem of Calculus.

[@peterdavidson987]

You're an amazing teacher. Thank you for all the vids. P.S I already liked, subbed, and told all my friends of your work.

[@Salehalanazi-7]

Every single time I love you more, I never forget good people and be sure Mr. Tarrou

[@profrobbob]

Please share the love and my channel with everyone! As you share this channel, please remind them to like, sub and support the ads too:D

[@profrobbob]

I really appreciate the referral of my videos for your class! As long as the videos get watched through KZbin that would be amazing...and I would be honored to help co- teach your students with you:)

[@gechgech6612]

Thankyou profeser God Bless You!

[@profrobbob]

THANKS again Getachew Tujo !

[@LonelyDev71]

Best teacher ever.

[@henrix5044]

thank professer i wish i could have a teacher like you

[@profrobbob]

You're welcome Henry Reneau and now that you've subbed I can be your official KZbin teacher and teach you anytime, 24/7, you need help...BAM!!! So "SPREAD THE WORD" :D

[@henrix5044]

thanks your a good teacher an i like math but my math teacher dont explain it correctly but thanks tu you evrything is good. :)

[@profrobbob]

Henry Reneau BAM!!! Keep up the good work:)

[@arminamargaryan4510]

Thank YOU So sO much!!! I like your way of teaching.And very much appreciate your help!!! This will help me on my test. Thanks again...

[@13r1d3r]

Your videos are very helpful !!! wish you were my professor!!!

[@profrobbob]

Thanks for watching. You can sub and share with your friends and classmates and I can at least be your KZbin teacher...BAM!!!

[@michaelfeduccia7989]

BAM!! I'm gonna ace my exam tomorrow! Thank you Sir!

[@profrobbob]

You're welcome...thanks for studying with Tarrou's Chalk Talk! Don't forget to sub and share this free resource with friends, classmates and teachers too:D

[@Severemc]

Thanks so much for your videos. If it wasn't for you I would be doing much worse in my College Algebra class. Keep up the great videos!

[@vaishalib4938]

Thank you sir! Your lecture was very clear and useful ! :)

[@profrobbob]

You're welcome...thanks for liking and learning..please sub and share too:D

[@profrobbob]

You're welcome!

[@tseringchoedon6866]

You are amazing....Moreover, I love your handwriting...

[@brirayborn9014]

at the y(x+2) point of the second example, why do you divide by x+2 instead of distributing the y to each number inside the parenthesis?

[@pothuruaneesh23]

Thank You! Helped me a lot professor!

[@profrobbob]

You're welcome Aneesh Pothuru thanks for choosing, subbing and learning!

[@parmanandsingh5797]

Bada-bing bada bang. BAM!!!! Go do your homework. Excellent demonstration of how to deal with inverse functions. Have to do some inverse trig functions now, then we're coomplete.

[@profrobbob]

BAM!!! Evaluating Inverse Trigonometric Functions Full Length

[@MsYarkpawolo]

Speechless. You are just good.

[@profrobbob]

I just answered your last comment...good to see you are already watching more Emmette Richardson ...don't forget to SUBSCRIBE and support the ads too!

[@kellynobleza5033]

do you have plane area by integration? if you have please comment here the link.. you have really help me by these videos thanks a lot

[@jocelynreyesh238]

Thanks for that awesome explanation !!that helped me A LOT !!!!!

[@profrobbob]

+Jocelyn Reyes thanks for studying and subbing!

[@anar1314]

Thank you SO much. You're excellent!

[@profrobbob]

You're welcome and thank for studying and subbing! Keep spreading the word:D

[@makeup4evr1]

you're video are sooo helpful :) !

[@profrobbob]

makeup4evr1 thanks for watching, learning, liking and subbing too!

[@mohammadfadayi3818]

great I understand all of them because of your marvelous explantion THANKS ALOT

[@profrobbob]

You're welcome Mohamad Fada thanks for watching and learning from #ProfRobBob !

[@profrobbob]

x=x/2? Did you mean y=x/2 and you want the inverse of that function?

[@heathermiller5413]

I love you prof Rob Bob...

[@profrobbob]

THANKS for studying, subbing and loving this channel please spread the word thru social media, friends, classmates and teachers so EVERYONE will sub and share and we can continue to grow and help others for free...BAM!!!

[@XSilverful]

I have a question for you. What is the point of this algebra math? How does this function in the world? Like, with graphing lines and shapes. I study a lot about the Phi ratio and how it can be found in all life forms. The mathematical blue print of the universe, but with this math I can't see the bigger picture for it. I feel like there is a missing link. Maybe you can help me out. :) How do you see this connecting with life? And, can you link this math with Phi?

[@bethanyymariee]

Do you have any videos where you talk about changing the domain of functions to make their inverse a function as well?

[@profrobbob]

No I do not. You need to restrict the domain so the original function is a 1 to 1 function. Like a parabola, you would want to remove say the left side of the parabola. Can you give me a specific example of a question you are working on?

[@bethanyymariee]

Oh, okay I think i get it! so for like x^2 i would just make the domain x is greater than or equal to 0, and it would work?

[@profrobbob]

Yes, Bethany Gardner you are absolutely correct...BAM!!!

[@eddie4071]

you deserve more subscribers...

[@profrobbob]

THANKS for being one of them...got any ideas how can we make that happen?

[@eddie4071]

ProfRobBob you should make an interesting thumbnail or a short intro vedio to engage people

[@Tinydude10]

Great video. I got everything you talked about, but I'm having trouble with a more challenging problem like the inverse function of y = sqrt(2x+1), which require domain limitations. Understanding those graphically is OK, but algebraically negative square roots and the like make my head spin. Do you have any videos which could help with that?

[@profrobbob]

With your original problem 2x+1 must be greater than or equal to zero. Subtract 1 and divide by two and the restricted domain is x>= -1/2 The restricted domain of the original function will become the restricted range of the inverse function since you are effectively swapping the x & y's when setting up an inverse.

[@profrobbob]

The range of y = sqrt(2x+1) is y>=0 because you are only going to accept the positive square roots as your equation states. The range of the original function becomes the domain of the inverse.

[@Tinydude10]

ProfRobBob Thank you very much for that! I think the main thing that helped me here is the range and domain reversal. It seems as long as you find the range for the original function you're pretty much cleared for any domain restrictions you need to do for the inverse. Which makes a whole lot of sense, it just eluded me up to now.

[@profrobbob]

Tinydude10 You're very welcome! Keep studying like you are and you'll "get it all" and soon be ready to help your friends too:) Check out my video on Inverse Trig Functions for more examples:)

[@profrobbob]

BAM!!! I like hearing that:)

[@shyamsubramanian9094]

Thanks so much! Your videos are lot more helpful than reading from the textbook! Are you a College Algebra professor?

[@profrobbob]

You're welcome Shyam…I'm glad you are finding my videos so helpful and hope you are telling your friends about my channel as well! I've taught high school math (mostly upper lever) at the same school for 18 years…and this channel for 2, as you may have guessed…I love teaching!

[@profrobbob]

BAM!!!!...that's what I'm talkin about!!!

[@12iLovEuFc12]

What College/University do you teach?

[@NoANaga]

Not to be rude, but did you mean to say "Vertical line" instead of "Horizontal line". You said this @4:23

[@profrobbob]

Yes...thank you:):):)

[@nadinemarcel7229]

could u do a video on how to prove that a function is surjective and injective if u have the time please? thank u n keep up the good work!!

[@profrobbob]

I apologize, but I am doing everything I can just to stay ahead of my new AP Calculus AB class this year!!! Thank you for your kind words:)

[@kendracooper6723]

I would like to use your videos as a "supplemental source" for my Pre-Calc class but I would like to ask permission first... may I do this? I tell the students that they can find you on KZbin but I just wanted to get your permission to use them in my actual class :)

[@ericwilliams3734]

Aw Yeahgh baby! Now we're twist-turning these functions... with ease!

[@profrobbob]

BAM!!! we are:) Eric Williams

[@memexo1751]

what is the inverse function of F^-1(T) when T={3, 5, 4} ? is it {-3, -5, -4}?