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 graph. The y - value when x = 0 is 4. So $f(0)=4$.

Step2: Find x when f(x)=0

Look for the x - value where the graph intersects the x - axis. The graph of y = f(x) intersects the x - axis at x = 2. So when $f(x)=0$, $x = 2$.

Step3: Recall inverse - function property

The inverse function $y = f^{-1}(x)$ has the property that if $y = f(x)$, then $x = f^{-1}(y)$. When $f(x)=0$ at $x = 2$, then $f^{-1}(0)=2$.

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

If $f^{-1}(x)=0$, then by the property of inverse functions, $f(0)=x$. Since $f(0)=4$, when $f^{-1}(x)=0$, $x = 4$.

Answer:

$f(0)=4$
$f(x)=0,x = 2$
$f^{-1}(0)=2$
$f^{-1}(x)=0,x = 4$