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I need help with this problem (composite functions):

If f(x) = 4x-3 and h(x )= 4x^2-21, find a function g such that f(g(x)) = h.

I don't understand how we're supposed to combine the functions.

Oh, and the answer is supposed to be g(x) = x^2 - (9/2).

Thanks!

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2 answers
  1. I was reading, and got the answer in my head before I read your answer line.

    It is easy.

    f(x) is given. 4x-3 YOu want 4x^2-21

    so what times 4 will equal 4x^2? Ans x^2

    Now what times 4 will equal -21 when you add -3? 4z-3=-21
    4z=-18
    z=-9/2

    so g(x)=x^2 -9/2

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    bobpursley
  2. 4 x 3 = 12
    21 – 2 = 19
    4 x 2 = 8
    5 x 4 = 20
    2 + 1 = 3
    14 x 12 = 168
    4 x 12 = 48
    2 + 4 = 6

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