Solution
= Solution
Because $x\mapsto c^Tx$ is a <linear map>,
$$
g(tx+(1-t)y)
=f(tc^Tx+(1-t)c^Ty)
\leq tf(c^Tx)+(1-t)f(c^Ty).
$$
\b[Hence composition of a convex function with an affine map is convex, and $g$ is convex.]
= Solution
Because $x\mapsto c^Tx$ is a <linear map>,
$$
g(tx+(1-t)y)
=f(tc^Tx+(1-t)c^Ty)
\leq tf(c^Tx)+(1-t)f(c^Ty).
$$
\b[Hence composition of a convex function with an affine map is convex, and $g$ is convex.]