Question

the function f(x) is invertible. find $f^{-1}(0)$.
$f^{-1}(0)=\square$

Explanation:

Step1: Recall the inverse function property

The inverse function \( f^{-1}(y) \) gives the \( x \)-value such that \( f(x) = y \). So, to find \( f^{-1}(0) \), we need to find the \( x \)-value where \( f(x) = 0 \).

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

Looking at the graph of \( f(x) \), we find the point where the graph intersects the \( x \)-axis (since at the \( x \)-axis, \( y = 0 \)). From the graph, we can see that the graph of \( f(x) \) crosses the \( x \)-axis at \( x = 1 \) (by visually inspecting the grid, the intersection point is at \( (1, 0) \)). This means \( f(1) = 0 \).

Step3: Use the inverse function definition

Since \( f(1) = 0 \), by the definition of the inverse function, \( f^{-1}(0) = 1 \).

Answer:

\( 1 \)