Answer: They are inverses of each other============================================================Explanation:We need to check two things:f(g(x)) = xg(f(x)) = xIf both of those equations are true, then f and g are inverses of each other.----------------Part 1[tex]f(x) = -3x-12\\\\f(g(x)) = -3( g(x) )-12\\\\f(g(x)) = -3\left( \frac{-12-x}{3} \right)-12\\\\f(g(x)) = 12+x-12\\\\f(g(x)) = x\\\\[/tex]So far, so good. Now we need to check the other equation mentioned.------------------Part 2[tex]g(x) = \frac{-12-x}{3}\\\\g(f(x)) = \frac{-12-( f(x) )}{3}\\\\g(f(x)) = \frac{-12-( -3x-12 )}{3}\\\\g(f(x)) = \frac{-12+3x+12}{3}\\\\g(f(x)) = \frac{3x}{3}\\\\g(f(x)) = x\\\\[/tex]That works out as well. Both equations mentioned are true, which confirms the two original functions are inverses of one another.