Suppose that $f(x)=4x+5$. What is $f^{-1}(f^{-1}(9))$?
To find $f^{-1}(f^{-1}(9))$, I need to first find $f^{-1}(9)$ and then apply $f^{-1}$ to that result. That means I need to subtract $5$ from $9$ and then divide by $4$. So, $f^{-1}(9) = \frac{9-5}{4} = 1$. So, $f^{-1}(f^{-1}(9)) = \frac{1-5}{4} = -1$. 