Show that 2 is a relaxation of 1 if and only if the

Question

An optimization problem(1)can be viewed as defining a function: S → R, where S is the feasible set of (1).

The epigraph of f is the set {(z, x) | z ≥ f(x), x ∈ S}.

Show that (2) is a relaxation of (1) if and only if the projection of the epigraph of f' onto (z, x) contains the epigraph of f. ¹