Question

If `f(x)=-2x+11` and `g(x)=x-6`, how do you find `[fog](x)` and `[gof](x)`?

Answer 1

The answers are `fog(x)=-2x+23` and `gof(x)=-2x+5`

Explanation:

`f(x)=-2x+11`

`g(x)=x-6`

`fog(x)=f(g(x))=f(x-6)=-2(x-6)+11`
`=-2x+12+11=-2x+23`

`gof(x)=g(f(x))=g(-2x+11)=-2x+11-6`
`=-2x+5`

I think that the equations speak by themselves.

Of course, `fog(x)!=gof(x)`