# How to find the inverse of a piecewise function

How would I go about finding the inverse of a piecewise function? In this case the function is

$$f(x) = \left\{ \begin{array}{lr} x, & \text{if } 0\leq x \leq 1,\\ x-1, & \text{if } 2 < x \leq 3. \end{array} \right.$$

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You have $y=x$ when $0 \le x \le 1$ and $y=x-1$ when $2 < x \le 3,$ which is to say when $1<y\le 2$ since $y=x-1$. And the inverse function is obtained by switching $x$ and $y$. So when $0 \le y \le 1$ the inverse value is $y$, while when $1<y\le 2$ the inverse value is $y+1$.