Restrict the Domain of the Function F So That the Function

question 3

Multiple Choice

Restrict the domain of the function f so that the function is one-to-one and has an in- verse function. Then find the inverse function $f ^ { - 1 }$ . State the domains and ranges of f and $f ^ { - 1 }$ . $f ( x ) = ( x - 2 ) ^ { 2 }$

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

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Definitions:

Fixed Manufacturing Overhead

The portion of manufacturing overhead costs that do not vary with the level of production or sales, such as factory rent.

Fixed Manufacturing Overhead

Costs that do not change with the level of production, such as rent, salaries, and insurance for the manufacturing facilities.

Budget Variance

The difference between the budgeted or baseline amount of expense or revenue, and the actual amount.

Insurance Rates

The cost per unit of coverage set by insurance companies, determining the premium paid by policyholders.