Question

find (f o g) (x) and (g o f) (x) and the domain of each. f(x)=x+5, g(x)=x-5

Answer 1

We are given the following two functions

$\begin{gathered} f(x)=x+5 \\ g(x)=x-5 \end{gathered}$

First, let us find out (fog) (x)

$\begin{gathered} (f\circ g)(x)=(x-5)+5 \\ (f\circ g)(x)=x-5+5 \\ (f\circ g)(x)=x \end{gathered}$

The domain is all the possible values of x.

$domain=(-\infty,\infty)$

Similarly, let us find out (gof) (x)

$\begin{gathered} (g\circ f)(x)=(x+5)-5 \\ (g\circ f)(x)=x+5-5 \\ (g\circ f)(x)=x \end{gathered}$

The domain is all the possible values of x.

$domain=(-\infty,\infty)$