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 28

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.

---

Definitions:

Consultation Rights

Rights that allow employees or their representatives to be consulted on workplace matters affecting them before decisions are made.

European Works Council

A workforce consultation body set up in multinational companies operating within the European Economic Area (EEA) for the purpose of informing and consulting employees on transnational issues affecting them.

Deferred Action

A discretionary, temporary relief from deportation granted by the Department of Homeland Security to eligible individuals who lack a lawful immigration status.

Deportation

The formal removal of a person from a country where they are not a citizen due to legal violations or threat to public safety.