With a given [[Function]], $f: X\to Y$, if $Y \subseteq X$ then the function can be [[Composition|Composed]] multiple times. $\huge \begin{align} f^2(x) &= (f\circ f)(x)\\ f^3(x) &= (f\circ f\circ f)(x) \\ f^n(x) &= \underbrace{(f \circ f \circ \cdots )}_{n \text{ times}}(x) \\ f^n(x) &= \pa{\mathop{\bigcirc}_{i=1}^{n} f}(x) \end{align} $ When $n$ is 0 for any [[Function]], that function $f^{0}(x)$ is the [[Identity]] of $fs [[Domain]] $\op{id}_{X}$. **If** $f$ is [[Inverse Function|Invertible]], when $n < 0$ the statement is equal to the $n$th power of the [[Inverse Function]] of $f$. $\huge f^{-n} = \underbrace{f^{-1} \circ f^{-1} \circ \cdots}_{n \text{ times}} = \pa{f^{-1}}^n $