Question

Find the domains of (f o g)(x) and (g o f)(x).
f(x)=x/(x-7) g(x)= -6/(x+1)

Answer 1

\[dom(fog)=\left\{ x|x \neq-1,x \neq-13/7 \right\}\]

Answer 2

\[dom(gof)=\left\{ x|x \neq7 \right\}\]

Answer 3

Justification for answers above:

For dom(fog), x first has to be good in function g. That means x can't be -1. Further, when we substitute g(x) into f, g(x) can't be seven. That gives us the restriction x not -13/7.

For dom(gof), the first place x has to go is f, so x can't be seven. f(x) won't ever be negative one, so there are no further restrictions.