Composite functions and their domains (KristaKingMath)

Поделиться
HTML-код
  • Опубликовано: 30 окт 2024
  • ► 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.
    ● ● ● GET EXTRA HELP ● ● ●
    If you could use some extra help with your math class, then check out Krista’s website // www.kristakingm...
    ● ● ● 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.kristakingm...
    FACEBOOK // / kristakingmath
    TWITTER // / kristakingmath
    INSTAGRAM // / kristakingmath
    PINTEREST // / kristakingmath
    GOOGLE+ // plus.google.co...
    QUORA // www.quora.com/...

Комментарии • 327

  • @boboganbobogan9297
    @boboganbobogan9297 2 года назад +1

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

    • @kristakingmath
      @kristakingmath  2 года назад +1

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

  • @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! :)

  • @kristakingmath
    @kristakingmath  12 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! :)

  • @Tasniaaaaaaaa
    @Tasniaaaaaaaa 12 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.

  • @r3g4rds
    @r3g4rds 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).

  • @kristakingmath
    @kristakingmath  11 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. :)

  • @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.

  • @MegaSchoolgirls
    @MegaSchoolgirls 10 лет назад

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

  • @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. :)

  • @AbdulkareemAlnoaman
    @AbdulkareemAlnoaman 7 лет назад +1

    Good job explaining the composed functions and finding their domains.

  • @pietrom2
    @pietrom2 9 лет назад +1

    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.

  • @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

  • @reid0415
    @reid0415 9 лет назад +2

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

    • @kristakingmath
      @kristakingmath  9 лет назад

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

  • @kristakingmath
    @kristakingmath  12 лет назад +1

    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 4 года назад

      Burklow yeah 2 months ago lol 😆

  • @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

  • @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.

  • @saaniyahsajed1932
    @saaniyahsajed1932 6 лет назад

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

    • @kristakingmath
      @kristakingmath  6 лет назад

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

  • @kristakingmath
    @kristakingmath  12 лет назад

    Glad you liked the video!

  • @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

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

  • @kristakingmath
    @kristakingmath  11 лет назад

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

  • @kristakingmath
    @kristakingmath  11 лет назад

    I'm so glad you like it! :)

  • @kristakingmath
    @kristakingmath  11 лет назад

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

  • @richardstern2460
    @richardstern2460 8 лет назад

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

  • @brittneysosa7250
    @brittneysosa7250 11 лет назад

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

    • @kristakingmath
      @kristakingmath  11 лет назад

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

  • @Kowboy1911
    @Kowboy1911 11 лет назад

    Way better than my Trig teacher. Thank you so much

  • @chaoticneutral8040
    @chaoticneutral8040 9 лет назад

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

    • @kristakingmath
      @kristakingmath  9 лет назад +1

      Chaos Earthquake I'm so glad it helped!!

  • @vincentortega4284
    @vincentortega4284 5 лет назад

    Awesome! Krista. Great teaching thank you.

  • @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!

  • @MrNdour1116
    @MrNdour1116 12 лет назад

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

  • @lehlohonolotlhako5938
    @lehlohonolotlhako5938 7 лет назад +2

    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

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

  • @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.

  • @kristakingmath
    @kristakingmath  11 лет назад

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

  • @montyponty2
    @montyponty2 10 лет назад

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

    • @kristakingmath
      @kristakingmath  10 лет назад +1

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

  • @whumbo7whale
    @whumbo7whale 12 лет назад

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

  • @antonyfidelis
    @antonyfidelis 10 лет назад

    I liked the way you explained. Thank you!

  • @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 👍👍👍👍👍

  • @TheSoundLab.
    @TheSoundLab. 8 лет назад

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

    • @kristakingmath
      @kristakingmath  8 лет назад +1

      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

  • @snarlboomer
    @snarlboomer 11 лет назад

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

  • @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!

  • @bibiangallegos1647
    @bibiangallegos1647 11 лет назад +50

    I have no future D: I don't understand

  • @GregorysMode
    @GregorysMode 8 лет назад

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

  • @kamyarfatahi8265
    @kamyarfatahi8265 4 года назад

    You and your explanation are beautiful ❤️

  • @kristakingmath
    @kristakingmath  12 лет назад

    Glad I could help!

  • @lo0over4
    @lo0over4 12 лет назад

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

  • @kristakingmath
    @kristakingmath  11 лет назад

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

  • @Daniel-fb1qd
    @Daniel-fb1qd 11 лет назад

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

  • @kristakingmath
    @kristakingmath  11 лет назад

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

  • @reaganhesse3757
    @reaganhesse3757 10 лет назад

    Great job very helpful and clear keep making videos

  • @amirazamtb
    @amirazamtb 12 лет назад

    Thanks, really cleared things up for me.

  • @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! :)

  • @paulablue142
    @paulablue142 8 лет назад +8

    YOU JUST SAVED ME FROM DOOM. THANK YOU SO MUCH

  • @CF-pb1ev
    @CF-pb1ev 8 лет назад

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

  • @kristakingmath
    @kristakingmath  12 лет назад

    I can't find any!! :( And I haven't made one. In fact, I haven't run into that kind of problem before. If I run across something, I'll let you know, otherwise I'll try to make one after I dig into it a little bit.

  • @andyjac22
    @andyjac22 11 лет назад

    Unbelievable, you just saved my life.

  • @muhammadzafar2470
    @muhammadzafar2470 8 лет назад +1

    very best explanation.
    i love you Miss.

  • @youmanaa
    @youmanaa 6 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

  • @rturae
    @rturae 11 лет назад

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

  • @muhassin11
    @muhassin11 12 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!

  • @kristakingmath
    @kristakingmath  12 лет назад

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

  • @mlondinzimande5770
    @mlondinzimande5770 6 лет назад

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

  • @kristakingmath
    @kristakingmath  11 лет назад

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

  • @rsanch09
    @rsanch09 9 лет назад +1

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

  • @kristakingmath
    @kristakingmath  12 лет назад

    Glad I could help! :)

  • @raejohnson2647
    @raejohnson2647 8 лет назад

    Thank you for this helpful video!

  • @kaileyjones2548
    @kaileyjones2548 11 лет назад

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

  • @kristakingmath
    @kristakingmath  11 лет назад

    I'm so glad I could help! :D

  • @kyleseager9883
    @kyleseager9883 8 лет назад

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

    • @kristakingmath
      @kristakingmath  8 лет назад

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

  • @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

  • @kristakingmath
    @kristakingmath  11 лет назад

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

  • @AmandeepSingh-yy7ed
    @AmandeepSingh-yy7ed 4 года назад

    It's very useful for me thanks teacher👩‍🏫‍

    • @kristakingmath
      @kristakingmath  4 года назад

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

  • @reogomez
    @reogomez 8 лет назад +2

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

  • @shivashishsarkar8584
    @shivashishsarkar8584 10 лет назад

    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?

  • @turrd88
    @turrd88 11 лет назад

    prettiest teacher on youtube, thanks a lot :)

  • @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?

  • @kristakingmath
    @kristakingmath  12 лет назад

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

  • @Seabass1Jazz
    @Seabass1Jazz 10 лет назад

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

  • @kristakingmath
    @kristakingmath  11 лет назад

    You're welcome! :)

  • @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??

  • @kristakingmath
    @kristakingmath  11 лет назад

    I hope so too! Good luck! :)

  • @kristakingmath
    @kristakingmath  11 лет назад

    You're so welcome! :)

  • @dontjinxme
    @dontjinxme 11 лет назад

    Exactly the question I was going to ask her. I am thinking that it would be (-infin,-1)U(-1,-2)U(-2, infin) infin=infinity. But again, it was going to be my question. Did you find an answer?

  • @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.

  • @NotALie12
    @NotALie12 10 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. :/

  • @epistrophy9919
    @epistrophy9919 9 лет назад

    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?

  • @sailinginwatersailinginwat2682
    @sailinginwatersailinginwat2682 6 лет назад

    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

  • @kristakingmath
    @kristakingmath  11 лет назад

    Awesome!

  • @the07vlog86
    @the07vlog86 9 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.

  • @Billy-rk2kp
    @Billy-rk2kp 10 лет назад +1

    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

  • @kristakingmath
    @kristakingmath  12 лет назад

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

  • @missmania2700
    @missmania2700 10 лет назад

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

  • @2112201211
    @2112201211 10 лет назад +1

    Greetings from Brazil! Great classes and no doubts left!

  • @gogetta90001
    @gogetta90001 10 лет назад

    I'm confused at 2:40
    How can x+1/x+2 be simplified by x+1, shouldn't it be simplified by x+2 reducing it to X+1? same type of confusing on the other side.

  • @kristakingmath
    @kristakingmath  12 лет назад

    Hey thanks!

  • @daniakhatib6214
    @daniakhatib6214 11 лет назад

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

  • @TheFiuza22
    @TheFiuza22 11 лет назад

    i love this teacher

  • @kristakingmath
    @kristakingmath  12 лет назад

    Good luck on your upcoming final! :)

  • @drewstunner
    @drewstunner 12 лет назад

    This video really help thank you so much :)

  • @kristakingmath
    @kristakingmath  11 лет назад

    awesome! Glad I could help. :)