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Math Help - composite functions

  1. #1
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    composite functions

    Hello,

    I've done this question but i am not sure if its correct.

    Given that f(x)= 2x+1 and g(x)=3x-5 find the value of

    a) fg(0) b) gg(4)

    ---Answer---

    a) fg(0)= f(g(0))

    g(0)= 3(0)-5

    = - 2

    f(-2)= 2(-2)+1

    =-3

    b) gg(4)= g(g(4))

    g(4)= 3(4)-5

    =7

    f(4)= 2(7)+1

    =15

    Is my way and answer correct?

    Thanks.
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  2. #2
    A riddle wrapped in an enigma
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    Quote Originally Posted by Oasis1993 View Post
    Hello,

    I've done this question but i am not sure if its correct.

    Given that f(x)= 2x+1 and g(x)=3x-5 find the value of

    a) fg(0) b) gg(4)

    ---Answer---

    a) fg(0)= f(g(0))

    g(0)= 3(0)-5 <=== 0 - 5 = -5

    = - 2 <===-5

    f(-2)= 2(-2)+1 <=== f(-5) = 2(-5) + 1

    =-3 <=== = -9

    b) gg(4)= g(g(4))

    g(4)= 3(4)-5

    =7

    f(4)= 2(7)+1 <==== your problem b) says g(g(4)), not f(g(4)). If g(4) = 7, then g(7)=3(7)-5 or 16.

    =15

    Is my way and answer correct?

    Thanks.
    Hi Oasis1993,

    See corrections in red.
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  3. #3
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    Ive made some careless mistakes.
    Thanks for your help!
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  4. #4
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    And please try to distinguish better between the product of two functions, fg, and the composition fog or gof.
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