Help please

For some constants $a$ and $b,$ let \[f(x) = \left\{ \begin{array}{cl} 9 - 2x & \text{if } x \le 3, \\ ax + b & \text{if } x > 3. \end{array} \right.\]The function $f$ has the property that $f(f(x)) = x$ for all $x.$ What is $a + b?$