Question

use the graph below to fill in the missing values. f(0)= f(x)=0, x= f^(-1)(0)= f^(-1)(x)=0, x= question help: video

Explanation:

Step1: Find f(0)

Look at x = 0 on the x - axis. The corresponding y - value on the graph of y = f(x) is 3. So f(0)=3.

Step2: Find x when f(x)=0

Find the x - value where the graph of y = f(x) intersects the x - axis. The graph intersects the x - axis at x = 5. So when f(x)=0, x = 5.

Step3: Recall the property of inverse function

If y = f(x) and x = f^{-1}(y), then f^{-1}(0) is the x - value such that f(x)=0. From Step 2, f^{-1}(0)=5.

Step4: Find x when f^{-1}(x)=0

If f^{-1}(x)=0, then x is the value of f(0). From Step 1, when f^{-1}(x)=0, x = 3.

Answer:

f(0)=3
f(x)=0, x = 5
f^{-1}(0)=5
f^{-1}(x)=0, x = 3