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# For some constants $a$ and $b,$ let The function $f$ has the property that $f(f(x)) = x$ for all $x.$ What is $a + b?$

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$$f(x) = \left\{ \begin{array}{cl} ax + b & \text{if } x < 2, \\ 8 - 3x & \text{if } x \ge 2. \end{array} \right.$$

Dec 15, 2020

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a = 3 and b = 8, so a + b = 11.

Dec 15, 2020