The Function F Is One-To-One $$f ( x ) = ( x + 2 ) ^ { 3 } - 8$$

question 267

Multiple Choice

The function f is one-to-one. Find its inverse.
- $$f ( x ) = ( x + 2 ) ^ { 3 } - 8$$

• A) \(f ^ { - 1 } ( x ) = \sqrt [ 3 ] { x + 6 }\)
• B) \(f ^ { - 1 } ( x ) = \sqrt [ 3 ] { x - 2 } + 8\)
• C) \(f ^ { - 1 } ( x ) = \sqrt [ 3 ] { x + 10 }\)
• D) \(\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \sqrt [ 3 ] { \mathrm { x } + 8 } - 2\)

---

Definitions:

Depressive Disorder

A category of mood disorders characterized by persistent feelings of sadness, hopelessness, and a lack of interest or pleasure in daily activities.

Psychological Pain

A form of suffering that arises from non-physical sources, often related to emotional distress, mental health disorders, or existential concerns.

General "Depression"

A common mental health disorder characterized by persistent sadness, loss of interest in activities, and an inability to carry out daily tasks.

Manic Episode

A period of abnormally elevated or irritable mood, arousal, and/or energy levels, frequently found in bipolar disorder.