Math (Grade 12)
posted by Lucy on .
I need help with this problem (composite functions):
If f(x) = 4x3 and h(x )= 4x^221, 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!

I was reading, and got the answer in my head before I read your answer line.
It is easy.
f(x) is given. 4x3 YOu want 4x^221
so what times 4 will equal 4x^2? Ans x^2
Now what times 4 will equal 21 when you add 3? 4z3=21
4z=18
z=9/2
so g(x)=x^2 9/2 
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