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Composite functions and their domains (KristaKingMath) 

Krista King
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► 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
FACEBOOK // / kristakingmath
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INSTAGRAM // / kristakingmath
PINTEREST // / kristakingmath
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QUORA // www.quora.com/profile/Krista-...

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28 июл 2012

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Комментарии : 329   
@RacingLights
@RacingLights 11 лет назад
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
@boboganbobogan9297
@boboganbobogan9297 2 года назад
I have no words to describe how brilliant this explanation was. Thank you very very much!!
@kristakingmath
@kristakingmath 2 года назад
You're very welcome, I'm so glad you liked it! :D
@Tasniaaaaaaaa
@Tasniaaaaaaaa 11 лет назад
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
@kristakingmath 12 лет назад
Thanks for the feedback! The same certainly can't be said for my earlier videos, but I've tried to improve over time. :)
@MegaSchoolgirls
@MegaSchoolgirls 10 лет назад
Omg thank you for explaining the domain for an advance problem!! I couldn't find an explanation anywhere.
@turrd88
@turrd88 11 лет назад
prettiest teacher on youtube, thanks a lot :)
@kristakingmath
@kristakingmath 11 лет назад
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! :)
@rainonedavid3564
@rainonedavid3564 4 года назад
I'm in algebra II. This video was way more definitive than the videos I was supposed to watch, thanks.
@kristakingmath
@kristakingmath 11 лет назад
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! :)
@reid0415
@reid0415 8 лет назад
Your videos helps me a lot. So much thanks. :) Continue to spread your wonderful ideas and knowledge!
@kristakingmath
@kristakingmath 8 лет назад
+Enzo celecio Aw thanks! I'm happy I can help.
@pietrom2
@pietrom2 9 лет назад
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.
@SuperKris50
@SuperKris50 11 лет назад
Way better than my Trig teacher. Thank you so much
@gaymo69
@gaymo69 12 лет назад
Your videos are very professional and clearly articulated (i.e., without any ums and ahs, which are rife in most other instructional math videos).
@snarlboomer
@snarlboomer 11 лет назад
Brilliant! Thanks for making these videos. I love how your passion for the maths shines though.
@brittneysosa7250
@brittneysosa7250 10 лет назад
You are a LIFE saver! I had spent an hour trying to understand this :D You rock! Thanks for helping!
@kristakingmath
@kristakingmath 10 лет назад
I'm so glad it makes sense now!! You're welcome!! :D
@AbdulkareemAlnoaman
@AbdulkareemAlnoaman 7 лет назад
Good job explaining the composed functions and finding their domains.
@MrNdour1116
@MrNdour1116 11 лет назад
Your a godsend!! And you had the happiest greeting!
@kristakingmath
@kristakingmath 11 лет назад
I'm glad I've been able to help!
@kristakingmath
@kristakingmath 10 лет назад
That's so awesome! I'm so glad I could help. :)
@kristakingmath
@kristakingmath 11 лет назад
I'm so glad I could help! :D
@kristakingmath
@kristakingmath 11 лет назад
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
@KEVIN11534 4 года назад
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
@KEVIN11534 3 года назад
Burklow yeah 2 months ago lol 😆
@saaniyahsajed1932
@saaniyahsajed1932 5 лет назад
this helps so much! i was so confused for the longest time. you resolved it. thank you!
@kristakingmath
@kristakingmath 5 лет назад
You're welcome, I'm so glad it makes more sense now! :D
@lehlohonolotlhako5938
@lehlohonolotlhako5938 7 лет назад
Hey krista that was really helpful,can you please create one where you explain how to find a range(composite function).
@kristakingmath
@kristakingmath 11 лет назад
Yay!!! So glad I could help. :)
@tanishjeetsingh4350
@tanishjeetsingh4350 7 лет назад
Thank you for patiently working every single step. It really helped me. You're explanation is the probably best in the world.
@kristakingmath
@kristakingmath 7 лет назад
I'm so glad it could help!
@paulablue142
@paulablue142 8 лет назад
YOU JUST SAVED ME FROM DOOM. THANK YOU SO MUCH
@kristakingmath
@kristakingmath 8 лет назад
You're welcome, I'm so glad it helped!
@Daniel-fb1qd
@Daniel-fb1qd 10 лет назад
This helped me soooo much for my pre-calculus class thank you sooooo much :)
@rsanch09
@rsanch09 8 лет назад
WOW! Thank you so much for the amazing explanation. My light bulb just turned on!
@kristakingmath
@kristakingmath 10 лет назад
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. :)
@bibiangallegos1647
@bibiangallegos1647 10 лет назад
I have no future D: I don't understand
@AYDEN3
@AYDEN3 9 лет назад
You're literally saving me in pre calc 12 for summer school! Thanks a ton! :)
@kristakingmath
@kristakingmath 9 лет назад
Ayden Yeung You're welcome, I'm so glad the videos are helping!
@kristakingmath
@kristakingmath 11 лет назад
that's very sweet of you to say! thank you so much!! :D
@HisBelovedQueen
@HisBelovedQueen 10 лет назад
How do I find out Range? this helped a lot thanks!!!
@richardstern2460
@richardstern2460 7 лет назад
Great work... Really cleared up the fog on finding domain of a composition and the steps to find it. Eeeasy ,,, Peeeasy!
@kristakingmath
@kristakingmath 7 лет назад
I'm so glad it could help!
@kristakingmath
@kristakingmath 11 лет назад
Glad I could help!
@kristakingmath
@kristakingmath 10 лет назад
you're welcome! i'm so glad it was helpful!! :D
@vincentortega4284
@vincentortega4284 5 лет назад
Awesome! Krista. Great teaching thank you.
@kristakingmath
@kristakingmath 5 лет назад
Thanks, Vincent! So glad you liked it! :D
@gene546
@gene546 11 лет назад
thanks I have improved a lot as to started to get B+. Once again thanks for your dedication to educate others.
@whumbo7whale
@whumbo7whale 12 лет назад
Thanks! i like your vids way more than my teacher. Keep it up!
@kristakingmath
@kristakingmath 11 лет назад
you're welcome, i'm so glad you liked it!
@lo0over4
@lo0over4 11 лет назад
awesome video! Thanks so much for helping me! I finally understand how to find the domain now!
@kristakingmath
@kristakingmath 11 лет назад
you're welcome!! i'm so glad you liked it. :D
@kristakingmath
@kristakingmath 11 лет назад
I'm so glad you like it! :)
@kristakingmath
@kristakingmath 11 лет назад
you're welcome!! im' so glad it helped!! :D
@kristakingmath
@kristakingmath 11 лет назад
Glad I could help! :)
@kristakingmath
@kristakingmath 11 лет назад
Awesome! I'm so glad it helped. :)
@kristakingmath
@kristakingmath 11 лет назад
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
@kristakingmath 11 лет назад
i'm glad it helped! books can be so frustrating sometimes! :/
@kristakingmath
@kristakingmath 11 лет назад
you're welcome!! i'm so glad you liked it!! :D
@bookworm397
@bookworm397 10 лет назад
Really helpful. Thanks!
@siyabulelamanona1438
@siyabulelamanona1438 7 лет назад
thank you very. i think u might have forgotten to include some domains but thank you anyway your god sent.
@muhammadzafar2470
@muhammadzafar2470 7 лет назад
very best explanation. i love you Miss.
@kyleseager9883
@kyleseager9883 7 лет назад
Thank you so much!!!!! You literally saved me, thanks for the amazing video! It makes so much more sense!
@kristakingmath
@kristakingmath 7 лет назад
You're so welcome! I'm glad it could help!
@kristakingmath
@kristakingmath 11 лет назад
Awww love you too!! I'm so glad it helped!! :D
@CF-pb1ev
@CF-pb1ev 7 лет назад
Another very helpful video. Thank you so much, I've subscribed!
@kristakingmath
@kristakingmath 7 лет назад
Thanks!
@missmania2700
@missmania2700 9 лет назад
Thank you for your help! You explain this sooo well! :) I totally get it!
@kristakingmath
@kristakingmath 9 лет назад
Awesome! Glad I could help.
@kristakingmath
@kristakingmath 11 лет назад
Good luck on your upcoming final! :)
@chaoticneutral8040
@chaoticneutral8040 9 лет назад
You cleared this up for me, thank you very much!
@kristakingmath
@kristakingmath 9 лет назад
Chaos Earthquake I'm so glad it helped!!
@kaileyjones2548
@kaileyjones2548 10 лет назад
Thank you so much!! I was so confused but now I understand it!!!
@kamyarfatahi8265
@kamyarfatahi8265 4 года назад
You and your explanation are beautiful ❤️
@ritu7235
@ritu7235 4 года назад
Nice concept krista.....i m able to clear my doubts.... excellent .....
@kristakingmath
@kristakingmath 4 года назад
Thanks, Shankar, I'm so glad it helped! :)
@kristakingmath
@kristakingmath 11 лет назад
Awww you're sweet! I'm glad it helped you!! :D
@kristakingmath
@kristakingmath 12 лет назад
Glad you liked the video!
@mlondinzimande5770
@mlondinzimande5770 6 лет назад
hey, I am from South Africa, Thank you for the awesome video. In Zulu We say "Ngiyabonga-Thank you"
@antonyfidelis
@antonyfidelis 10 лет назад
I liked the way you explained. Thank you!
@kristakingmath
@kristakingmath 10 лет назад
you're welcome!
@MoizAMarvi1
@MoizAMarvi1 8 лет назад
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?
@daniakhatib6214
@daniakhatib6214 11 лет назад
VERY HELPFUL!!!!!! :)and love your hair style!! so cutee
@amirazamtb
@amirazamtb 11 лет назад
Thanks, really cleared things up for me.
@kristakingmath
@kristakingmath 11 лет назад
awesome! Glad I could help. :)
@reogomez
@reogomez 8 лет назад
Not only a fantastic teacher but a beatiful, beatiful girl... OMG..... Thanks Krista!!
@muhassin11
@muhassin11 11 лет назад
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!
@montyponty2
@montyponty2 9 лет назад
thank you so much. this cleared up so many issues for me!!
@kristakingmath
@kristakingmath 9 лет назад
you're welcome, i'm so glad it helped!!
@gamersamista477
@gamersamista477 9 лет назад
Thank u so much helped me a lot
@amandeepsingh-xz3js
@amandeepsingh-xz3js 7 лет назад
you are a awesome teacher...you done a great job of teaching ...keep it up makes more videos we like u 👍👍👍👍👍
@coach2779
@coach2779 3 года назад
better math teacher than my math teacher lmao. thank you
@kristakingmath
@kristakingmath 3 года назад
You're welcome, FaZe, I'm so glad I'm able to help!
@kristakingmath
@kristakingmath 10 лет назад
You're so welcome! :)
@andyjac22
@andyjac22 10 лет назад
Unbelievable, you just saved my life.
@kristakingmath
@kristakingmath 10 лет назад
Awesome!! :D
@youmanaa
@youmanaa 5 лет назад
This helped me so much, thank you!!
@kristakingmath
@kristakingmath 5 лет назад
You're welcome, Youmana, I'm so glad it helped! :D
@GregorysMode
@GregorysMode 8 лет назад
Superb thanks Krista, my tutor just said "plug in" you were much clearer. Tar
@kristakingmath
@kristakingmath 8 лет назад
I'm so glad I could help!
@kristakingmath
@kristakingmath 10 лет назад
I hope so too! Good luck! :)
@kristakingmath
@kristakingmath 11 лет назад
i'm so glad you liked the video! :D
@naimulhaq9626
@naimulhaq9626 10 лет назад
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.
@the.misanthropist
@the.misanthropist 8 лет назад
thanks a lot. You explained it better than my professor did
@kristakingmath
@kristakingmath 8 лет назад
+Tamara M You're welcome, I'm so glad it made sense!
@sanjeevsiva17
@sanjeevsiva17 9 лет назад
hmmmm....really enjoyin learning math through all you videos :) i am going to subscribe (y)
@rturae
@rturae 11 лет назад
Thank you so much. You just saved me from a big headache :)
@drewstunner
@drewstunner 11 лет назад
This video really help thank you so much :)
@the07vlog86
@the07vlog86 8 лет назад
how can you solve 3/×-1=8 is there a website where they can explain to me step by step? i really want to learn so i can help my sister with her homework thanks.
@raejohnson2647
@raejohnson2647 8 лет назад
Thank you for this helpful video!
@kristakingmath
@kristakingmath 8 лет назад
You're welcome! Glad it could help!
@TheSoundLab.
@TheSoundLab. 8 лет назад
You're my maths guru. Thank you very much.
@kristakingmath
@kristakingmath 8 лет назад
You're welcome, I'm so glad you've been enjoying the videos!
@TheSoundLab.
@TheSoundLab. 8 лет назад
Big thanks to you, my exam pretty well. Thank you very much for your help.
@kristakingmath
@kristakingmath 8 лет назад
Great job! I'm so glad to hear it, thanks for letting me know! :D
@Billy-rk2kp
@Billy-rk2kp 9 лет назад
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
@NotALie12
@NotALie12 9 лет назад
how can the domain of f(g(x)) be written in interval notation? I was having trouble with that part in my class. :/
@aishashabbir9911
@aishashabbir9911 10 лет назад
INTEGRAL CALC UUUUUUUUUUUU RRRRRRRRRR AWESOMMMMME I actually got this i thought I will fail my Precalculus test hopefully I pass my test also.
@rm9994
@rm9994 2 года назад
Excellent Kristy. After 5:47 I get a little confused. Any videos to practice that stuff? Thanks, all the best
@JazminZenteno1
@JazminZenteno1 8 лет назад
at 2:24 how do we know when we should flip them and why does the one go away?
@reaganhesse3757
@reaganhesse3757 9 лет назад
Great job very helpful and clear keep making videos
@kristakingmath
@kristakingmath 9 лет назад
thank you!!
@kristakingmath
@kristakingmath 11 лет назад
Awesome!
@craigbell9273
@craigbell9273 6 лет назад
Krista do you do graphing of complex composition of functions
@MsIkkiPikki
@MsIkkiPikki 10 лет назад
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??
@xoxUnD3R0aThxox
@xoxUnD3R0aThxox 10 лет назад
so if i was writing the domain as interval, the final domain will be the union or the intersection of the two domains?
@SuperLfcforlife
@SuperLfcforlife 12 лет назад
that's great :) thanks for the video! lovely writing i must say