Restrict the Domain of the Function F So That the Function

question 54

Multiple Choice

Restrict the domain of the function f so that the function is one-to-one and has an inverse function.Then find the inverse function f^-1.State the domains and ranges of f and f^-1. ?
F(x) = (x - 5) ²
?

• A) \(f ^ { - 1 } ( x ) = \sqrt { x } - 5\) ?
• The domain of f and the range of f^-1 are all real numbers x such that x ? 5.The domain of f^-1 and the range of f are all real numbers x such that x ? 0.
• B) \(f ^ { - 1 } ( x ) = \sqrt { x } + 5\) ?
• The domain of f and the range of f^-1 are all real numbers x such that x ? 0.The domain of f^-1 and the range of f are all real numbers x such that x ? -5.
• C) \(f ^ { - 1 } ( x ) = \sqrt { x } + 5\) ?
• The domain of f and the range of f^-1 are all real numbers x such that x ? 5.The domain of f^-1 and the range of f are all real numbers x such that x ? 0.
• D) \(f ^ { - 1 } ( x ) = \sqrt { x } + 5\) ?
• The domain of f and the range of f^-1 are all real numbers x such that x ? 0.The domain of f^-1 and the range of f are all real numbers x such that x ? 5.
• E) \(f ^ { - 1 } ( x ) = \sqrt { x } - 5\) ?
• The domain of f and the range of f^-1 are all real numbers x such that x ? -5.The domain of f^-1 and the range of f are all real numbers x such that x ? 0.

---

Definitions:

Private Practice

The practice of a health care provider or clinic operating independently, offering services to individuals on a fee-for-service basis.

Community Mental Health Centre

A facility that provides mental health services, including therapy and counseling, to people in a local area.

Deinstitutionalization

Refers to the process of reducing the use of large, institutional facilities for people with mental health issues in favor of community-based mental health care services.

Severe Mental Illness

A term referring to a group of psychiatric disorders that significantly interfere with one’s ability to function in daily life.