Finding the domain of a function

Question

Given  and , find the domain of 

Answer 1

f(x) = 1 / (x-2) and g(x) = 2 / (x+3)

domain of f(g(x)) = {x l x is in domain g and g(x) is in domain f}

= {x l x ≠ -3 and 2 / (x+3) ≠ 2} = {x l x ≠ -3 and 2(x+3) ≠ 2} = {x l x≠-3 and x ≠ -2}