Browse · MATH Print → jmc algebra intermediate Problem Suppose that f(x) and g(x) are functions which satisfy f(g(x))=x2 and g(f(x))=x3 for all x≥1. If g(16)=16, then compute [g(4)]3. Solution — click to reveal Setting x=4 in f(g(x))=x2, we get f(g(4))=16.Then g(f(g(4))=g(16)=16.But g(f(g(4))=[g(4)]3, so [g(4)]3=16. Final answer 16 ← Previous problem Next problem →