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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.

Question 28

Multiple Choice

Determine whether the function has an inverse function.If it does,find the 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.


A) f−1(x) ={x−138,x<−2x+3−2,x≥−2f ^ { - 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) ={x−138,x<−2x+1,x≥−2f ^ { - 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) ={x−138,x<−3x+3−2,x≥−3f ^ { - 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) ={x+138,x<−3x+3−2,x≥−3f ^ { - 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.

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