If the Function Is One-To-One, Find Its Inverse $$f ( x ) = ( x - 6 ) ^ { 2 }$$

question 315

Multiple Choice

If the function is one-to-one, find its inverse. If not, write "not one-to-one."
- $$f ( x ) = ( x - 6 ) ^ { 2 }$$

• A) not a one-to-one
• B) \(f ^ { - 1 } ( x ) = \frac { 1 } { \sqrt { x + 6 } }\)
• C) \(\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \sqrt { \mathrm { x } + 6 }\)
• D) \(f ^ { - 1 } ( x ) = \sqrt { x } + 6\)

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Definitions:

Splitting

A defense mechanism often associated with borderline personality disorder, characterized by viewing people or situations as all good or all bad.

Antisocial Personality Disorder

A mental condition characterized by a long-term pattern of manipulating, exploiting, or violating the rights of others.

Callous Attitude

Showing a lack of empathy or concern for others, often characterized by insensitivity or indifference to others' feelings.

Reclusive Behavior

The tendency to seek isolation and avoid social interaction, often seen in individuals who experience high levels of stress or those who have mental health conditions.