Question

the function f(x) is invertible. find $f^{-1}(2)$.
$f^{-1}(2) = \square$

Explanation:

Step1: Recall inverse function definition

The inverse function \( f^{-1}(y) \) gives the \( x \)-value such that \( f(x) = y \). So, to find \( f^{-1}(2) \), we need to find \( x \) where \( f(x) = 2 \).

Step2: Analyze the graph of \( f(x) \)

Looking at the graph of \( f(x) \), we find the point where the \( y \)-coordinate is 2. From the grid, when \( y = 2 \), the corresponding \( x \)-value is 1 (by observing the graph's coordinates: the curve passes through \( (1, 2) \) since at \( x = 1 \), \( y = 2 \)).

Answer:

\( f^{-1}(2) = 1 \)