Given an MLE $\hat{\theta}$, how to show $f(\hat{\theta})$ is also an MLE?

Question

Given an injective function $f: \Theta \rightarrow \mathbb{R}$ and an MLE $\hat{\theta}$ of $\theta ^*$, how do I prove that $f(\hat{\theta})$ is an MLE of $f(\theta^*)$. I know that because $f$ is injective, we can say

$L(\theta ^*) = L(f^{-1}(f(\theta ^*)))$. But I do not know how to use this in the proof.