Logic: building a sentence

Logic: building a sentence

Let $L$ be a language with a 1-place function symbol $f$. Give an
$L$-sentence $\phi$ that is true in every $L$-structure $M$ if the
following holds: if $M \models \phi$, then $M$ is infinite.
My idea is to construct a sentence that, given $n$ different variables,
all the values of those variables under the evaluation of $f$, must be
different. Is this a good way to stary? Any help will be much appreciated!