a) For f(g) just replace x in f = 3x-12 by x/3+4, thus

f(g(x)) = 3((x/3)+4) -12 = x

b) similarly g(f(x)) = 1/3(3x-12)+4 = x.

c) From a and b, f(g(x)) = g(f(x)) = x, and they have the same domain of R, so g(x) = f^-1(x) and f= g^-1(x) we see that function f and g are inverses of each other.