Question

Let `f(x) = x + 8` and `g(x) = 3x`, how do you find each of the compositions and domain and range?

Answer 1

The compositons are `f(g(x))=3x+8` Domain ∈`RR` Range ∈`RR`
and `g(f(x))=3x+24` Domain ∈`RR` Range∈ `RR`

Explanation:

`f(x)=x+8`

`g(x)=3x`

Replace x by 3x in g(x)
`fog(x)= f(g(x))=f(3x)=3x+8`
the domain is `RR`
and the range `RR`

Replace x by (x+8) in g(x)
`gof(x)=g(f(x))=g(x+8)=3(x+8)=3x+24`
the domain is `RR`
and the range `RR`

You can see that `f(g(x))!=g(f(x))`