Find the Inverse of the Function $f ( x ) = - x ^ { 2 } + 12 , x \geq 0$

question 210

Multiple Choice

Find the inverse of the function.
- $f ( x ) = - x ^ { 2 } + 12 , x \geq 0$

• A) \(\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \sqrt { 12 - \mathrm { x } }\)
• B) \(f ^ { - 1 } ( x ) = x ^ { 2 } + 12\)
• C) \(f ^ { - 1 } ( x ) = \sqrt { x + 12 }\)
• D) \(f ^ { - 1 } ( x ) = - \sqrt { x ^ { 2 } + 12 }\)

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Definitions:

Producer Surplus

The gap between the minimum amount producers are willing to accept for providing a good or service and the actual amount they end up receiving.

Producer Surplus

The additional income a producer receives for selling a good or service above its production cost.

Tax

A tax is a compulsory financial charge or some other type of levy imposed upon a taxpayer by a governmental organization.

Consumer Surplus

The discrepancy between the amount consumers are prepared to spend on a product or service and the actual price they pay.