Question

the graph of a one - to - one function f is given. draw the graph of the inverse function f^(-1). for convenience (and as a hint), the graph of y = x is also given. choose the correct graph of the inverse function f^(-1) below.

Explanation:

Step1: Recall inverse - function property

The graph of a one - to - one function \(y = f(x)\) and its inverse \(y = f^{-1}(x)\) are symmetric about the line \(y=x\). That is, if \((a,b)\) is on the graph of \(y = f(x)\), then \((b,a)\) is on the graph of \(y = f^{-1}(x)\).

Step2: Analyze key points

Identify some key points on the graph of \(y = f(x)\). For each point \((x_0,y_0)\) on \(y = f(x)\), plot the point \((y_0,x_0)\) on the graph of \(y = f^{-1}(x)\) and then connect these new points to form the graph of the inverse function.

Since we don't have the actual coordinates of the points on the original function graph in a numerical form, we rely on the symmetry about \(y = x\). Visually, we can see that the correct graph of the inverse function should be the one that is the mirror - image of the given function graph with respect to the line \(y=x\).

Answer:

(Without seeing the actual options clearly, we can't give a specific letter - option. But the correct option is the one where the graph is symmetric to the given \(f(x)\) graph about the line \(y = x\))