Help finding the domain

Find the domains of (FoG)(x) and (GoF)(x)

f(x) = x^2 - 7; g(x) = 1/(x+6)

Can someone show me all the steps to solving this?

(FoG)(x) = g(x)^2 - 7 = [1/(x+6)]^2 + 7
Domain: x not = 6

(GoF)(x) = 1/(f(x)+6) = 1/(x^2 - 1)
Domain: x not = +/- 1

fog(x) = {1/(x + 6)}^2 - 7 = {1 - 7x^2 - 84x - 252}/(x + 6)^2 ;

gof(x) = 1/{x^2 - 1} = 1/(x+1)(x - 1) ;

fog(x) is undefined at x = - 6 and gof(x) is undefined at x = - 1 and x = 1 .