Question

F(x) =2x-4 and g(x) =-3x+2 find: f(g(x))

Answer 1

`f(g(x))=-6x`

Explanation:

Composite Function

Given f(x) and g(x) as real functions, the composite function named
`(f\circ g)(x)` is defined as:

`(f\circ g)(x)=f(g(x))`

It can simply be found by substituting g into f.

Our functions are:

`f(x)=2x-4`

`g(x)=-3x+2`

Substituting g into f:

`f(g(x))=2(-3x+2)-4`

Operating:

`f(g(x))=-6x+4-4`

Simplifying:

`\boxed{f(g(x))=-6x}`