You have linear functions p(x) and q(x) . You know p(2) = 3, and p(q(x)) = -4x + 7 for all x. Find q(1).

Since p(q(x)) = - 4x +3, we must have p(q(1)) = -4(1) +7 =3. We also know that p(2) = 3=p(q(1)). Since p, being linear, is a one-to-one function, it follows that q(1) = 2.