Exercise 38, § 2

Let X be a convex set of an affine space E and $p$ an affine linear mapping of E in a second affine linear space $E_1$. Write $X_1 = p(X)$. For every real-valued function $f$ defined in X and every $x_1 \in X_1$, let

Show that if $f$ is convex and if $f_1(x_1) > -\infty$ for all $x_1 \in X_1$, then $f_1$ is a convex function.