Determine whether the function has an inverse function.If it does, find the inverse function.
$f ( x ) = \left\{ \begin{array} { l }
x + 2 , x

Question

Determine whether the function has an inverse function.If it does, find the inverse function. 
 $f ( x ) = \left\{ \begin{array} { l } 
x + 2 , x < 0 \
2 - x , x \geq 0
\end{array} \right.$  
A) $f ^ { - 1 } ( x ) = \left\{ \begin{array} { l } 
2 + x , x \geq 0 \
x - 2 , x < 0
\end{array} \right.$
B) $f ^ { - 1 } ( x ) = \left\{ \begin{array} { l } 
2 + x , x \geq 0 \
x - 2 , x < 0
\end{array} \right.$.
C) $f ^ { - 1 } ( x ) = \left\{ \begin{array} { l } 
x - 2 , x \geq 0 \
2 + x , x < 0
\end{array} \right.$
D) $f ^ { - 1 } ( x ) = \left\{ \begin{array} { l } 
x + 2 , x \geq 0 \
2 - x , x < 0
\end{array} \right.$
E)No inverse

Quizplus · Accepted Answer

The function is not one-to-one because it is not strictly increasing or decreasing over its entire domain, hence it does not have an inverse.

Determine Whether the Function Has an Inverse Function f(x)={x+2,x<02−x,x≥0f ( x ) = \left\{ \begin{array} { l } x + 2 , x < 0 \\2 - x , x \geq 0\end{array} \right.f(x)={x+2,x<02−x,x≥0​

Determine Whether the Function Has an Inverse Function $f ( x ) = \left\{ \begin{array} { l } x + 2 , x < 0 \\2 - x , x \geq 0\end{array} \right.$