For some constants a and b let
\(f(x) = \left\{ \begin{array}{cl} ax + b & \text{if } x < 2, \\ 8 - 3x & \text{if } x \ge 2. \end{array} \right.\)
The function \(f\) has the property that \(f(f(x)) = x\) for all \(x\) What is \(a+b\)
+308 a(8-3x)+b=x
-3ax+8a+b=x
a would need to be -1/3 in order to keep the x term on the left isolated. 8a+b would need to be equal to 0, so be would be 8/3. 8/3+(-1/3)=7/3.
