Prove that $f(\cap\_{i\in I}X\_i)\subset\cap\_{i\in I}f(X\_i)$

From a second year calculus course. Have only done Basic Set Theory and Injective/Surjective functions. I'm thinking the proof has something to do with the injectivity of $f(\cap\_{i\in I}X\_i)$? 

Any help would be appreciated, thanks.