Logic: existence of a certain type of a bijective function on an infinite set

Logic: existence of a certain type of a bijective function on an infinite set

Let $X$ be an infinite set. Prove that there is a bijective function $f: X
\rightarrow X$ with the property that for every $x \in X$ and all $n > 0$:
$f^n(x) \neq x$.
I've tried to proved this by considering a bijective function $g:
\mathbb{Z} \times X \rightarrow X$ in a certain way (by the composition of
a function $f: \mathbb{Z} \times X \rightarrow \mathbb{Z} \times X$), but
that's all i've got at the moment.