The Function $f ( x ) = \sqrt { x ^ { 2 } - 6 }$

question 43

Multiple Choice

The function $f ( x ) = \sqrt { x ^ { 2 } - 6 }$ is one-to-one on the domain $x \leq - \sqrt { 6 }$ . Find $f ^ { - 1 } ( x )$ .

• A) \(f ^ { - 1 } ( x ) = - \sqrt { x ^ { 2 } - 6 }\)
• B) \(\quad f ^ { - 1 } ( x ) = - \sqrt { x ^ { 2 } + 6 }\)
• C) \(f ^ { - 1 } ( x ) = x ^ { 2 } + 6\)
• D) \(f ^ { - 1 } ( x ) = \frac { 1 } { \sqrt { x ^ { 2 } - 6 } }\)
• E)
• \[f ^ { - 1 } ( x ) = \sqrt { x ^ { 2 } + 6 }\]

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