Restrict the Domain of the Function F So That the Function

question 165

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) = -6x² + 2

• A) \(f ^ { - 1 } ( x ) = \frac { \sqrt { - 6 ( x - 2 ) } } { 6 }\) The domain of f and the range of f^-1 are all real numbers x such that x \(\ge\) 0.The domain of f^-1 and the range of f are all real numbers x such that x \(\le\) 2.
• B) \(f ^ { - 1 } ( x ) = \frac { \sqrt { - 2 ( x - 6 ) } } { 2 }\) The domain of f and the range of f^-1 are all real numbers x such that x \(\ge\) 0.The domain of f^-1 and the range of f are all real numbers x such that x\(\le\) 2.
• C) \(f ^ { - 1 } ( x ) = \frac { \sqrt { - 6 ( x - 2 ) } } { - 6 }\) The domain of f and the range of f^-1 are all real numbers x such that x \(\ge\) 0.The domain of f^-1 and the range of f are all real numbers x such that x \(\le\) 2.
• D) \(f ^ { - 1 } ( x ) = \frac { \sqrt { - 6 ( x - 2 ) } } { 6 }\) The domain of f and the range of f^-1 are all real numbers x such that x \(\ge\) 0.The domain of f^-1 and the range of f are all real numbers x such that x \(\le\) -2.
• E) \(f ^ { - 1 } ( x ) = \frac { \sqrt { - 6 ( x + 2 ) } } { 6 }\) The domain of f and the range of f^-1 are all real numbers x such that x \(\ge\) 0.The domain of f^-1 and the range of f are all real numbers x such that x \(\le\) 2.

Recognize the concept of marginal costs in environmental initiatives and its economic implications.

Comprehend the tragedy of the commons and its significance in environmental science and policy.

Grasp the role of government and regulatory agencies in establishing and enforcing environmental standards.

Understand the carbon tax system and its application in greenhouse gas emission reduction.

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Definitions:

Depression

A mental disorder marked by an enduring depressed state or a disinterest in usual activities, leading to significant challenges in routine life.

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Relating to the observable actions of individuals and the ways in which these actions can be influenced or changed.

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Protein sites located on cell membranes, primarily serotonin receptors, which are involved in transmitting signals within the brain.