COMC 2012 C Problem 1

Let f(x)=x^{2} and g(x)=3 x-8.

(a) Determine the values of f(2) and g(f(2)).

(b) Determine all values of x such that f(g(x))=g(f(x)).

(c) Let h(x)=3 x-r. Determine all values of r such that f(h(2))=h(f(2)).