Jensen's inequality for proving $E\left[\frac1X\right]\ge \frac1{E[X]}$ where $P(X\leq 0) = 0$

Question

Let $X$ be a positive random variable, i.e., $P(X\leq 0) = 0$. Argue that, $$E\Big[\frac{1}{X}\Big] \geq \frac{1}{E\Big[X\Big]}$$

Since Jensen's Inequality is $\phi(E[X]) \leq E[\phi(X)]$, where $\phi$ is convex, is the question as simple as letting $\phi(X) = \frac{1}{X}$?