The problem states that the function $f$ is a one-to-one function. (a) Given $f(4) = 3$, we need to find $f^{-1}(3)$. (b) Given $f^{-1}(-4) = -5$, we need to find $f(-5)$.

1. Problem Description

The problem states that the function $f$ is a one-to-one function.

(a) Given $f(4) = 3$, we need to find $f^{-1}(3)$.

(b) Given $f^{-1}(-4) = -5$, we need to find $f(-5)$.

2. Solution Steps

(a) We know that if $f(x) = y$, then $f^{-1}(y) = x$. Given $f(4) = 3$, we can find $f^{-1}(3)$ by letting $x=4$ and $y=3$. Then $f^{-1}(3) = 4$.

(b) We know that if $f^{-1}(x) = y$, then $f(y) = x$. Given $f^{-1}(-4) = -5$, we want to find $f(-5)$. By letting $x=-4$ and $y=-5$, then $f(-5) = -4$.

3. Final Answer

(a) 4

(b) -4