Chapter 2, Functions - Section 2.8 - One-to-One Functions and their Inverses - 2.8 Exercises - Page 262: 36

$f^{-1}(f^{-1}(0))$ = 4

First find where f(x) = 0. Since the function is one-to-one, f(5) = 0. Therefore $f^{-1}(f^{-1}(0))$ = $f^{-1}(5)$ Then find where f(x) = 5. Since the function is one-to-one, f(4) = 5. Therefore $f^{-1}(f^{-1}(0))$ = $f^{-1}(5)$ = 4