Question

Given f(x), find g(x) and h(x) such that f(x)=g(h(x)) and neither g(x) nor h(x) is solely x.f(x)= 5/-4x+3

Answer 1

Given the value of f(x):

`f(x)=(5)/(-4x+3)`

If:

`f(x)=g(h(x))`

We have that:

`g(h(x))=(5)/(-4x+3)`

To decompose the function, we will look at the function and check if we see any part that might look like a simpler function.

One part that looks like a function is:

`\Rightarrow-4x+3`

Therefore, let this become our h(x):

`h(x)=-4x+3`

Hence, the composite function becomes:

`g(h(x))=(5)/(h(x))`

Replacing h(x) with x, we have:

`g(x)=(5)/(x)`

ANSWER:

`\begin{gathered} g(x)=(5)/(x) \\ h(x)=-4x+3 \end{gathered}`