Determine whether the function has an inverse function.If it does, find the inverse function. $$f ( x ) = \left\{ \begin{array} { l }
8 x + 13 , x

Question

Determine whether the function has an inverse function.If it does, find the inverse function. $$f ( x ) = \left\{ \begin{array} { l } 
8 x + 13 , x < - 2 \
( x + 2 ) ^ { 2 } - 3 , x \geq - 2
\end{array} \right.$$
A) $f ^ { - 1 } ( x ) = \left\{ \begin{array} { l } 
\frac { x - 13 } { 8 } , x < - 2 \
\sqrt { x + 3 } - 2 , x \geq - 2
\end{array} \right.$
B)  $f ^ { - 1 } ( x ) = \left\{ \begin{array} { c } 
\frac { x - 13 } { 8 } , x < - 2 \
\sqrt { x + 1 } , x \geq - 2
\end{array} \right.$
C) $f ^ { - 1 } ( x ) = \left\{ \begin{array} { l } 
\frac { x - 13 } { 8 } , x < - 3 \
\sqrt { x + 3 } - 2 , x \geq - 3
\end{array} \right.$
D) $f ^ { - 1 } ( x ) = \left\{ \begin{array} { l } 
\frac { x + 13 } { 8 } , x < - 3 \
\sqrt { x + 3 } - 2 , x \geq - 3
\end{array} \right.$
E)No inverse function exists.

Quizplus · Accepted Answer

The Answer of Determine whether the function has an inverse function.If it does, find the inverse function. $$f ( x ) = \left\{ \begin{array} { l } 
8 x + 13 , x < - 2 \
( x + 2 ) ^ { 2 } - 3 , x \geq - 2
\end{array} \right.$$
A) $f ^ { - 1 } ( x ) = \left\{ \begin{array} { l } 
\frac { x - 13 } { 8 } , x < - 2 \
\sqrt { x + 3 } - 2 , x \geq - 2
\end{array} \right.$
B)  $f ^ { - 1 } ( x ) = \left\{ \begin{array} { c } 
\frac { x - 13 } { 8 } , x < - 2 \
\sqrt { x + 1 } , x \geq - 2
\end{array} \right.$
C) $f ^ { - 1 } ( x ) = \left\{ \begin{array} { l } 
\frac { x - 13 } { 8 } , x < - 3 \
\sqrt { x + 3 } - 2 , x \geq - 3
\end{array} \right.$
D) $f ^ { - 1 } ( x ) = \left\{ \begin{array} { l } 
\frac { x + 13 } { 8 } , x < - 3 \
\sqrt { x + 3 } - 2 , x \geq - 3
\end{array} \right.$
E)No inverse function exists.

Determine Whether the Function Has an Inverse Function f(x)={8x+13,x<−2(x+2)2−3,x≥−2f ( x ) = \left\{ \begin{array} { l } 8 x + 13 , x < - 2 \\( x + 2 ) ^ { 2 } - 3 , x \geq - 2\end{array} \right.f(x)={8x+13,x<−2(x+2)2−3,x≥−2​

Determine Whether the Function Has an Inverse Function $f ( x ) = \left\{ \begin{array} { l } 8 x + 13 , x < - 2 \\( x + 2 ) ^ { 2 } - 3 , x \geq - 2\end{array} \right.$