<s>[INST] ### Problem
You are given the following information:
- $f(2^a) = 3^a$
- $f(1) = 1$
- $f$ is continuous on the interval $[1,4]$, not including the endpoints
- For any integer $x$, $\exists$ an integer $y$ such that $f(x) = y$.
- $f(x) = f^{-1}(x)$

Which of the following must be true?[/INST]