I'm not sure exactly how to prove this given $g ≥ f$.
I'm able to understand the proof for "if a canonical maximization linear programming problem is unbounded then the dual canonical minimization linear programming problem is infeasible", where you prove by contradiction and assume that if the max is unbounded, then the dual min problem is feasible, and then go on to show that since f is unbounded, $f \rightarrow \infty$, and thus there exits no feasible value $g ≥ f$.
However I'm not sure how to do it for minimization problem is unbounded $\Leftrightarrow$ the dual maximization problem is infeasible