Question

the function f(x) is invertible. find $f^{-1}(-7)$.
$f^{-1}(-7) = \square$

Explanation:

Step1: Recall inverse function definition

The inverse function \( f^{-1}(y) \) gives the \( x \)-value such that \( f(x) = y \). So, to find \( f^{-1}(-7) \), we need to find \( x \) where \( f(x) = -7 \).

Step2: Analyze the graph

Looking at the graph of \( f(x) \), we identify the point where the \( y \)-coordinate is \( -7 \). From the grid, when \( y = -7 \), the corresponding \( x \)-coordinate is \( 3 \) (by observing the graph's position on the grid lines). So, if \( f(3) = -7 \), then by the definition of the inverse function, \( f^{-1}(-7) = 3 \).

Answer:

\( 3 \)