Question

use the graph below to fill in the missing values.

question help: video
f(0) =
f(x) = 0, x =
f^(-1)(0) =
f^(-1)(x) = 0, x =

Explanation:

Step1: Find f(0)

Look at the value of y - coordinate when x = 0 on the graph. When x = 0, the line intersects the y - axis at y = 3. So f(0)=3.

Step2: Find x when f(x)=0

Look for the x - coordinate when y = 0 on the graph. The line intersects the x - axis at x = 5. So when f(x)=0, x = 5.

Step3: Recall the property of inverse function

If f(a)=b, then \(f^{-1}(b)=a\). Since f(5)=0, then \(f^{-1}(0)=5\).

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

If \(f^{-1}(x)=0\), then by the property of inverse functions, f(0)=x. Since f(0)=3, then 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