for un-convex f we have $epi\,g =conv \,epi f$ for any convex function like $p(x)$ that $f(x)\ge p(x)$ do we have $g(x)\ge p(x)$?

Question

$f(x)$ is un-convex and we have $g(x)$ that $$epi \ g =conv \ epi \ f$$ for any convex function like $p(x)$ that $f(x)\ge p(x)$ prove that $$g(x)\ge p(x)$$