Question

How do you find `[fog](x)` and `[gof](x)` given `f(x)=1/2x-7` and `g(x)=x+6`?

Answer 1

The answers are `[fog] (x) =1/2x-4` and `[gof] (x)=1/2x-1`

Explanation:

This is a composition of functions

`f(x)=1/2x-7`

`g(x)=x+6`

`[fog] (x) =f(g(x))=f(x+6)=1/2(x+6)-7`

`=1/2x+3-7=1/2x-4`

`[gof] (x)=g(f(x))=g(1/2x-7)= 1/2x-7+6`

`=1/2x-1`