Mutual information when Y is a function of X

Question

Mutual Information is defined here. What is the mutual information $I(X;Y)$ when Y is a function of X, or vice versa? Can I see a proof?

Answer 1

Hint: You know that, in general, $I(X;Y)=H(X)-H(X|Y)=H(Y)-H(Y|X)$. When $Y$ is a function of $X$ (or viceversa) you should be able to write $H(Y|X)$, or $H(X|Y)$.