Question 104
A polynomial $p(x)$ with real coefficients is called a square if and only if it is not a constant and there exists a polynomial $q(x)$ with real coefficients such that $p(x) = q(x)^2$. Suppose that $f(x)$ and $g(x)$ are non-constant polynomials with real coefficients such that neither of them is a square, but $f(g(x))$ is. Show that $g(f(x))$ is not a square.