Question

given that $f(x)$ is a one-to-one function and $f(3)=-4$, $f(-1)=6$, and $f(2)=3$, find $f^{-1}(3)$. explain in 1 or 2 sentences how you know what the answer is. (10 points)
$\bigcirc$ 6
$\bigcirc$ 2
$\bigcirc$ -1
$\bigcirc$ $-4$

Explanation:

For a one-to-one function \( f(x) \), the inverse function \( f^{-1}(y) \) returns the \( x \)-value such that \( f(x) = y \). Here, we need \( f^{-1}(3) \), so we find the \( x \) where \( f(x)=3 \); given \( f(2)=3 \), this \( x \) is 2.

Answer:

○ 2