Question

How do you find `[fog](x)` and `[gof](x)` given `f(x)=x^2-9` and `g(x)=x+4`?

Answer 1

The answers are `fog(x)=x^2+8x+7` and `gof(x)=x^2-5`

Explanation:

`f(x)=x^2-9`

`g(x)=x+4`

`fog(x)=f(g(x))=f(x+4)=(x+4)^2-9=x^2+8x+7`

`gof(x)=g(f(x))=g(x^2-9)=x^2-9+4=x^2-5`

`fog(x)!=gof(x)`