How to prove that exponential of an expected value of a variable is less than the expected value of the exponential of the variable

Question

I am trying to prove the following:

$e^{E(x)} \le E(e^x)$ for a discrete random variable x.

I am stuck on how to proceed. None of the usual rules for expected value seem to apply for something like $f(E(x))$. Can I some help? Thanks!!

Answer 1

Exponent is a convex function. Use, as suggested in the comments, Jensen's inequality