Question 15
Suppose two functions $f(x)$ and $g(x)$ are defined for all $x$ such that $2 \lt x \lt 4$ and satisfy $2 \lt f(x) \lt 4$, $2 \lt g(x) \lt 4$, $f(g(x)) = g(f(x)) = x$ and $f(x) \cdot g(x) = x^{2}$ for all such values of $x$. Prove that $f(3) = g(3)$.