Composite functions and their domains (KristaKingMath)

► My Precalculus course: www.kristakingmath.com/precal...
Learn how to calculate the compositions of two functions, including f(g(x)), g(f(x)), f(f(x)), and g(g(x)). Then describe the domain of each composite function.
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If you could use some extra help with your math class, then check out Krista’s website // www.kristakingmath.com
● ● ● CONNECT WITH KRISTA ● ● ●
Hi, I’m Krista! I make math courses to keep you from banging your head against the wall. ;)
Math class was always so frustrating for me. I’d go to a class, spend hours on homework, and three days later have an “Ah-ha!” moment about how the problems worked that could have slashed my homework time in half. I’d think, “WHY didn’t my teacher just tell me this in the first place?!”
So I started tutoring to keep other people out of the same aggravating, time-sucking cycle. Since then, I’ve recorded tons of videos and written out cheat-sheet style notes and formula sheets to help every math student-from basic middle school classes to advanced college calculus-figure out what’s going on, understand the important concepts, and pass their classes, once and for all. Interested in getting help? Learn more here: www.kristakingmath.com
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QUORA // www.quora.com/profile/Krista-...

[@kristakingmath]

Thanks for the feedback! The same certainly can't be said for my earlier videos, but I've tried to improve over time. :)

[@boboganbobogan9297]

I have no words to describe how brilliant this explanation was. Thank you very very much!!

[@kristakingmath]

You're very welcome, I'm so glad you liked it! :D

[@RacingLights]

OMG you are the best teacher in the world. I literally got the "domains of composite functions" concept within 2 mins thanks to you! You're a miracle and you're a saviour of potential failures in life! You know what my teacher put as a note? "The domain of a composed function is either the same as the domain of the first function, or else lies inside it (overlaps of the range of the first function and domain of the second function)" - that shit's confusing. You explain it way easier. LOVE YOU

[@reid0415]

Your videos helps me a lot. So much thanks. :) Continue to spread your wonderful ideas and knowledge!

[@kristakingmath]

+Enzo celecio Aw thanks! I'm happy I can help.

[@snarlboomer]

Brilliant! Thanks for making these videos. I love how your passion for the maths shines though.

[@pietrom2]

You are really strong. Your command is fantastic. I missed out when you were converting the fractions so that they all had the lowest common denominator. Have to go back to basics. Thank you though.

[@AbdulkareemAlnoaman]

Good job explaining the composed functions and finding their domains.

[@kristakingmath]

I'm glad I've been able to help!

[@rainonedavid3564]

I'm in algebra II. This video was way more definitive than the videos I was supposed to watch, thanks.

[@lehlohonolotlhako5938]

Hey krista that was really helpful,can you please create one where you explain how to find a range(composite function).

[@kristakingmath]

I'm so glad I could help! :D

[@kristakingmath]

That's so awesome! I'm so glad I could help. :)

[@brittneysosa7250]

You are a LIFE saver! I had spent an hour trying to understand this :D You rock! Thanks for helping!

[@kristakingmath]

I'm so glad it makes sense now!! You're welcome!! :D

[@Daniel-fb1qd]

This helped me soooo much for my pre-calculus class thank you sooooo much :)

[@kristakingmath]

Yay!!! So glad I could help. :)

[@saaniyahsajed1932]

this helps so much! i was so confused for the longest time. you resolved it. thank you!

[@kristakingmath]

You're welcome, I'm so glad it makes more sense now! :D

[@kristakingmath]

you're welcome, i'm so glad you liked it!

[@kristakingmath]

I'm so glad you like it! :)

[@kristakingmath]

that's very sweet of you to say! thank you so much!! :D

[@kristakingmath]

Glad I could help!

[@gaymo69]

Your videos are very professional and clearly articulated (i.e., without any ums and ahs, which are rife in most other instructional math videos).

[@tanishjeetsingh4350]

Thank you for patiently working every single step. It really helped me. You're explanation is the probably best in the world.

[@kristakingmath]

I'm so glad it could help!

[@MegaSchoolgirls]

Omg thank you for explaining the domain for an advance problem!! I couldn't find an explanation anywhere.

[@kristakingmath]

you're welcome!! i'm so glad you liked it. :D

[@kristakingmath]

you're welcome! i'm so glad it was helpful!! :D

[@kristakingmath]

you're welcome!! i'm so glad you liked it!! :D

[@kristakingmath]

Glad you liked the video!

[@lo0over4]

awesome video! Thanks so much for helping me! I finally understand how to find the domain now!

[@kristakingmath]

exactly. you multiply the x in the denominator of the third term by x/x. that would give you x^2/x + 1/x in the denominator. then, since you have a common denominator in the denominator, you can combine the fractions and get (x^2+1)/x. hope that helps! :)

[@kristakingmath]

you're welcome!! im' so glad it helped!! :D

[@bibiangallegos1647]

I have no future D: I don't understand

[@AYDEN3]

You're literally saving me in pre calc 12 for summer school! Thanks a ton! :)

[@kristakingmath]

Ayden Yeung You're welcome, I'm so glad the videos are helping!

[@kristakingmath]

Glad I could help! :)

[@rsanch09]

WOW! Thank you so much for the amazing explanation. My light bulb just turned on!

[@kristakingmath]

Awww! You're sweet! :) I'm glad it helped, and thanks for letting me know about the volume. I'm always trying to make it better. :D

[@KEVIN11534]

i need help with just one question f(x)=2xsquared or 2 above the x then -7+1 and g(x)=6x-5 i hope you can help ive seen soo many videos but none of them have examples like the problem in trying to solve

[@KEVIN11534]

Burklow yeah 2 months ago lol 😆

[@kristakingmath]

Awesome! I'm so glad it helped. :)

[@kaileyjones2548]

Thank you so much!! I was so confused but now I understand it!!!

[@vincentortega4284]

Awesome! Krista. Great teaching thank you.

[@kristakingmath]

Thanks, Vincent! So glad you liked it! :D

[@turrd88]

prettiest teacher on youtube, thanks a lot :)

[@kristakingmath]

Awww love you too!! I'm so glad it helped!! :D

[@Tasniaaaaaaaa]

I finally understand how to do it now!!! Thanks! And don't listen to the person who said that you confused them more; I don't think the process could be explained any better.

[@kristakingmath]

i'm glad it helped! books can be so frustrating sometimes! :/

[@kristakingmath]

You're so welcome! :)

[@HisBelovedQueen]

How do I find out Range? this helped a lot thanks!!!

[@kristakingmath]

1) depends on what your professor wants. i'd expect that they'd want you to simplify it, but you'd have to ask to be sure. 2) i think you have to simplify. for example, in this video when i found g(f(x)), i can't see any way to find the domain from the original functions. you'd have to simplify it to really be able to tell. basically, i think you're stuck with simplifying! :)

[@missmania2700]

Thank you for your help! You explain this sooo well! :) I totally get it!

[@kristakingmath]

Awesome! Glad I could help.

[@bookworm397]

Really helpful. Thanks!

[@kristakingmath]

Awww you're sweet! I'm glad it helped you!! :D

[@muhammadzafar2470]

very best explanation. i love you Miss.

[@gene546]

thanks I have improved a lot as to started to get B+. Once again thanks for your dedication to educate others.

[@kyleseager9883]

Thank you so much!!!!! You literally saved me, thanks for the amazing video! It makes so much more sense!

[@kristakingmath]

You're so welcome! I'm glad it could help!

[@kristakingmath]

awesome! Glad I could help. :)

[@kristakingmath]

Good luck on your upcoming final! :)

[@CF-pb1ev]

Another very helpful video. Thank you so much, I've subscribed!

[@kristakingmath]

Thanks!

[@kristakingmath]

I hope so too! Good luck! :)

[@amirazamtb]

Thanks, really cleared things up for me.

[@kristakingmath]

Hey thanks!

[@MrNdour1116]

Your a godsend!! And you had the happiest greeting!

[@kamyarfatahi8265]

You and your explanation are beautiful ❤️

[@kristakingmath]

Awesome!

[@paulablue142]

YOU JUST SAVED ME FROM DOOM. THANK YOU SO MUCH

[@kristakingmath]

You're welcome, I'm so glad it helped!

[@chaoticneutral8040]

You cleared this up for me, thank you very much!

[@kristakingmath]

Chaos Earthquake I'm so glad it helped!!

[@kristakingmath]

i'm so glad you liked the video! :D

[@gamersamista477]

Thank u so much helped me a lot

[@SuperKris50]

Way better than my Trig teacher. Thank you so much

[@bitchslapper12]

this is exactly the problem from my book, thank you!

[@mlondinzimande5770]

hey, I am from South Africa, Thank you for the awesome video. In Zulu We say "Ngiyabonga-Thank you"

[@kristakingmath]

In order to get a common denominator, you need both fractions to have a denominator of (x+1)(x+2). When you start, they each have only one of those factors, and you need them to have both factors so that you can combine them. Since the first fraction has a denominator of (x+2), and you need it to also have (x+1), you multiply the first fraction by (x+1)/(x+1), which will give you (x+1)(x+1) in the numerator, and (x+2)(x+1) in the denominator. :)

[@rturae]

Thank you so much. You just saved me from a big headache :)

[@antonyfidelis]

I liked the way you explained. Thank you!

[@kristakingmath]

you're welcome!

[@kristakingmath]

You're welcome! :)

[@kristakingmath]

Thanks! :)

[@mkusasakala3861]

good job! can you do a tutorial on graphing composite functions please.

[@montyponty2]

thank you so much. this cleared up so many issues for me!!

[@kristakingmath]

you're welcome, i'm so glad it helped!!

[@amandeepsingh-xz3js]

you are a awesome teacher...you done a great job of teaching ...keep it up makes more videos we like u 👍👍👍👍👍

[@youmanaa]

This helped me so much, thank you!!

[@kristakingmath]

You're welcome, Youmana, I'm so glad it helped! :D

[@drewstunner]

This video really help thank you so much :)

[@raejohnson2647]

Thank you for this helpful video!

[@kristakingmath]

You're welcome! Glad it could help!

[@kristakingmath]

ha...I'm not sure I quite fit that roll, but I'm happy I can help. :)

[@richardstern2460]

Great work... Really cleared up the fog on finding domain of a composition and the steps to find it. Eeeasy ,,, Peeeasy!

[@kristakingmath]

I'm so glad it could help!

[@kristakingmath]

awww thanks! :D

[@whumbo7whale]

Thanks! i like your vids way more than my teacher. Keep it up!

[@kristakingmath]

thanks! :)

[@ritu7235]

Nice concept krista.....i m able to clear my doubts.... excellent .....

[@kristakingmath]

Thanks, Shankar, I'm so glad it helped! :)

[@daniakhatib6214]

VERY HELPFUL!!!!!! :)and love your hair style!! so cutee

[@kristakingmath]

awww thanks!! :)

[@SuperLfcforlife]

that's great :) thanks for the video! lovely writing i must say

[@rm9994]

Excellent Kristy. After 5:47 I get a little confused. Any videos to practice that stuff? Thanks, all the best

[@kristakingmath]

awesome!! you're welcome!! :D

[@sanjeevsiva17]

hmmmm....really enjoyin learning math through all you videos :) i am going to subscribe (y)

[@reogomez]

Not only a fantastic teacher but a beatiful, beatiful girl... OMG..... Thanks Krista!!

[@MoizAMarvi1]

Hi there, thanks for the tutorials. In this video I didn't understand, how did you take LCD of polynomial when finding the domain of f o f. Please can you make me understand it?

[@muhassin11]

It was on my IGCSE past paper, and i was wondering how to do it!, but your Video here, helped me out , Thanks teach XD!

[@venkatlol6031]

Nice video and good explanation mam....

[@crayversace2804]

Really helpful thanks.

[@kristakingmath]

Awesome! Thanks for letting me know. :)

[@kristakingmath]

Awww don't get down on yourself... you can totally do it! :) If this video isn't making it click for you, try searching for some others on the same topic... maybe a different perspective will make more sense. I know it's tough, but I believe in you! :D

[@siyabulelamanona1438]

thank you very. i think u might have forgotten to include some domains but thank you anyway your god sent.

[@kristakingmath]

Oh good! :D

[@reaganhesse3757]

Great job very helpful and clear keep making videos

[@kristakingmath]

thank you!!

[@cheffington999]

THANKS SOOO MUCH!!!!