f(x)=x 3 −6f, left parenthesis, x, right parenthesis, equals, x, start superscript, 3, end superscript, minus, 6h(x)=\sqrt[\Large3]{2x-15}h(x)= 32x−15 h, left parenthesis, x, right parenthesis, equals, root, start index, 3, end index, square root of, 2, x, minus, 15, end square rootWrite f(h(x))f(h(x))f, left parenthesis, h, left parenthesis, x, right parenthesis, right parenthesis as an expression in terms of xxx.f(h(x))=f(h(x))=f, left parenthesis, h, left parenthesis, x, right parenthesis, right parenthesis, equals
Accepted Solution
A:
For this case we have the following functions: F (x) = x ^ 3-6 h (x) = 3 ^ root (2x-15) Doing the composition of functions we have: f (h (x)) = (3 ^ root (2x-15)) ^ 3-6 Rewriting we have: f (h (x)) = 2x-15 - 6 f (h (x)) = 2x-21 Answer: The compound function f (h (x)) is given by: f (h (x)) = 2x-21