I need help with this problem (composite functions):

Question

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!

Answer 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

Answer 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