Find the domains?????????

Find the domains of (F o G)(x) and (G o F)(x)

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

Can someone help me?

Substitute the other function for the argument .

(F o G)(x) = F( G (x) ) = [ 1/( x+6 ) ]² - 7 = 1 / ( x+6 )² - 7 ;

condition
x + 6 ≠ 0 ==> x ≠ -6 ;

The domain of (F o G) is R / { -6 } .

(G o F)(x) = G( F (x) ) = 1 / [ (x²-7) + 6 ] = 1 / ( x² - 1 ) ;

condition
x² - 1 ≠ 0 ==> x ≠ ± 1 ;

The domain of (G o F) is R / { -1 , 1} .