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

question 181

Multiple Choice

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.

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