Question

Find f(x) such that

h(x)= (fog)(x)
h(x)= (3-9x)^2
Describe
g(x)=
and
f(x)=

Answer 1

To derive h(x)=(3-9x)^2, choose g(x) as 3-9x and f(x) as the squaring function x^2, forming the composition f(g(x)) that equals h(x).

Step-by-step explanation:

To find the functions f(x) and g(x) such that h(x) equals the composition of f and g (denoted as (fog)(x)), where h(x) = (3-9x)^2, we need to determine two functions which when composed, result in h(x).

Let's start by assuming g(x) is the inner function and f(x) is the outer function in the composition. A simple choice for g(x) is the inner part of the expression given for h(x), which is g(x) = 3-9x.

Next, since h(x) is the square of g(x), we can choose f(x) to be a squaring function, namely f(x) = x^2. With these choices, (fog)(x) = f(g(x)) = f(3-9x) = (3-9x)^2, which is exactly the given h(x).