Composite functions and their domains (KristaKingMath)

► My Precalculus course: www.kristaking...
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.kristakingm...
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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.kristakingm...
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[@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

[@kristakingmath]

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

[@rainonedavid3564]

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

[@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.

[@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!

[@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! :)

[@MegaSchoolgirls]

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

[@turrd88]

prettiest teacher on youtube, thanks a lot :)

[@AbdulkareemAlnoaman]

Good job explaining the composed functions and finding their domains.

[@paulablue142]

YOU JUST SAVED ME FROM DOOM. THANK YOU SO MUCH

[@kristakingmath]

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

[@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.

[@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! :)

[@bibiangallegos1647]

I have no future D: I don't understand

[@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.

[@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. :)

[@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 😆

[@reogomez]

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

[@kristakingmath]

Glad you liked the video!

[@SuperKris50]

Way better than my Trig teacher. Thank you so much

[@kristakingmath]

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

[@kristakingmath]

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

[@lehlohonolotlhako5938]

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

[@gene546]

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

[@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

[@rsanch09]

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

[@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!

[@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

[@MrNdour1116]

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

[@kristakingmath]

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

[@kristakingmath]

I'm so glad you like it! :)

[@kristakingmath]

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

[@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]

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

[@kristakingmath]

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

[@siyabulelamanona1438]

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

[@rm9994]

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

[@kristakingmath]

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

[@whumbo7whale]

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

[@mlondinzimande5770]

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

[@kristakingmath]

Glad I could help!

[@Billy-rk2kp]

Shouldn't we figure the D of f and the R of g before solving (F o G) just to make sure that there is intersection between them ? because if there is no intersection the whole equation will be wrong

[@GregorysMode]

Superb thanks Krista, my tutor just said "plug in" you were much clearer. Tar

[@kristakingmath]

I'm so glad I could help!

[@the.misanthropist]

thanks a lot. You explained it better than my professor did

[@kristakingmath]

+Tamara M You're welcome, I'm so glad it made sense!

[@snarlboomer]

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

[@TheSoundLab.]

You're my maths guru. Thank you very much.

[@kristakingmath]

You're welcome, I'm so glad you've been enjoying the videos!

[@TheSoundLab.]

Big thanks to you, my exam pretty well. Thank you very much for your help.

[@kristakingmath]

Great job! I'm so glad to hear it, thanks for letting me know! :D

[@kristakingmath]

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

[@shivashishsarkar8584]

good one...can you clear one doubt for me??? My textbook says that when f:A to B and g:B to C: then (gof):A to C. What I am asking is that, does this condition always have to be satisfied: range of f is a subset of domain of g. I can understand that if the above condition is not satisfied, then the the composite function (gof) will not be A but a subset of A. You can choose to receive my question in the following form also: If the first function is defined from A to some set and the second function is defined from some set to C, then does the composite function have to have A as its domain? Is it compulsory?

[@andyjac22]

Unbelievable, you just saved my life.

[@kristakingmath]

Awesome!! :D

[@antonyfidelis]

I liked the way you explained. Thank you!

[@kristakingmath]

you're welcome!

[@vincentortega4284]

Awesome! Krista. Great teaching thank you.

[@kristakingmath]

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

[@kristakingmath]

I'm so glad I could help! :D

[@amandeepsingh-xz3js]

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

[@kristakingmath]

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

[@kristakingmath]

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

[@HisBelovedQueen]

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

[@kristakingmath]

Glad I could help! :)

[@epistrophy9919]

To Calculus expert. Below is a comment that for g o g , x cannot = -3/2 in addition to the values you suggest (x unequal to - 2 or x unequal to -5/3) (comment posted by Euler13 If I input -3/2 into the inside function I get -1 which makes the numerator of the outside function = 0, but not the denominator. So, do you agree that -3/2 is a solution or is not a solution?

[@muhammadzafar2470]

very best explanation. i love you Miss.

[@kristakingmath]

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

[@2112201211]

Greetings from Brazil! Great classes and no doubts left!

[@montyponty2]

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

[@kristakingmath]

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

[@coach2779]

better math teacher than my math teacher lmao. thank you

[@kristakingmath]

You're welcome, FaZe, I'm so glad I'm able to help!

[@Daniel-fb1qd]

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

[@kristakingmath]

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

[@chaoticneutral8040]

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

[@kristakingmath]

Chaos Earthquake I'm so glad it helped!!

[@amirazamtb]

Thanks, really cleared things up for me.

[@rturae]

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

[@lo0over4]

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

[@naimulhaq9626]

Duals are important in mathematics. In x(1-x)=0, x is dual of 1-x. Every Platonic figures has duals. How are "inverse" and "opposites" relate to "duals" ? I wish you had a video explaining them. I love your videos.

[@kamyarfatahi8265]

You and your explanation are beautiful ❤️

[@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?

[@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!

[@CF-pb1ev]

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

[@kristakingmath]

Thanks!

[@kristakingmath]

Awesome!

[@sailinginwatersailinginwat2682]

f(x) =sqrt(x+1), with a restricted domain of [0, infinity), h(x) = x^2+3, with a domain of R, to find the range of the composite function f(h(x)), the domain would be the domain of the inner function, h(x), which is R, but do we also need to take into account the domain of the outer function, f(x), which is [0, infinity)? Please explain reasoning g(x) = x^2+4x+4,with a restricted domain of (-infinity, -3], to find the range of the composite function, f(g(x)), the domain of f(g(x)) would be the domain of g(x), which is restricted to (-infinity, -3], but do we also need to take into account the domain of f(x), which is restricted to [0, infinity)? Please explain reasoning Thanks

[@rachelhuston7429]

yeah still dont know lol i give up

[@flamezcoleclarke4616]

dont give up tho

[@kristakingmath]

You're so welcome! :)

[@kristakingmath]

I hope so too! Good luck! :)

[@reaganhesse3757]

Great job very helpful and clear keep making videos

[@kristakingmath]

thank you!!

[@melodiecuevas9131]

I still have a question so for the first problem, how did you get x+1 times x+1 ?? And the denominator, I understand it but after the third step I am completely lost:? How did you get the common denominater?? Thanks :)

[@Seabass1Jazz]

pretty and smart .... wow. This world needs more of you

[@kennybassarath7168]

Krista, You are the best and easy on the eyes too.

[@kristakingmath]

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

[@kaileyjones2548]

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

[@kristakingmath]

Yes, I just get in the zone when I'm writing and forget to talk like a normal person! :)

[@ritu7235]

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

[@kristakingmath]

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

[@youmanaa]

This helped me so much, thank you!!

[@kristakingmath]

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

[@kristakingmath]

Hey thanks!

[@kristakingmath]

awesome! Glad I could help. :)

[@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. :)

[@MsIkkiPikki]

i am confused... when finding (f o f), f(f(x)), y did you multiply x+(1/x)+((x)/((x^2)+1) by the random nummbers like (X/x) and (((x^2)+1) /((x^2)+1) ) at the same time? Can't you do that once with x/x and then multiply (((x^2)+1) /((x^2)+1) ) afterwards , or does that change the denominator??

[@PokegurlMisty]

i trust u with my life

[@bookworm397]

Really helpful. Thanks!

[@kristakingmath]

You're welcome! :)

[@missmania2700]

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

[@kristakingmath]

Awesome! Glad I could help.

[@maryt.8043]

That's a lot easier than calculating the domain using set 😅😅 EDIT: my tutor says this technique is wrong. You should always calculate the domain of composite function using set, or you may miss something that cannot be taken from the final function