Question 85
Let $\mathbb{R}$ be the set of real numbers. Find all $a\gt 0$ such that there exists a function $f: \mathbb{R} \rightarrow \mathbb{R}$ with the following two properties:
a) $f(x)=a x+1-a$ for any $x \in [2,3)$;
b) $f(f(x))=3-2 x$ for any $x \in \mathbb{R}$.
a) $f(x)=a x+1-a$ for any $x \in [2,3)$;
b) $f(f(x))=3-2 x$ for any $x \in \mathbb{R}$.