### Instruction: Suppose $f(x)$ is an invertible function, and suppose that $f(2)=f^{-1}(2)=4$.

What is the value of $f(f(2))$?### Response: I need to find $f(f(2))$, which is the same as $f(4)$, since $f(2)=4$.
But I also know that $f^{-1}(2)=4$, which means that $f(4)=2$, by the definition of inverse functions.
So, $f(f(2))=f(4)=2$.