Browse · harp Print → smc algebra intermediate Problem If m, n, p, and q are real numbers and f(x)=mx+n and g(x)=px+q, then the equation f(g(x))=g(f(x)) has a solution (A) for all choices of mnp, and q (B) if and only if m=p and n=q (C) if and only if mq−np=0 (D) if and only if n(1−p)−q(1−m)=0 Solution — click to reveal f(g(x)=g(f(x))⟹m(px+q)+n=p(mx+n)+q This simplifies to mq+n=pn+q or n(1−p)−q(1−m)=0. The answer is if and only if n(1−p)−q(1−m)=0. Final answer D ← Previous problem Next problem →