The Function F(x) = X² - 2 Is One-To-One on the Domain

question 307

Multiple Choice

The function f(x) = x² - 2 is one-to-one on the domain (x $\le$ 0) .Find f ^-1(x) .

• A) \(f ^ { - 1 } ( x ) = - \sqrt { x + 2 }\)
• B) \(f ^ { - 1 } ( x ) = \frac { 1 } { x ^ { 2 } - 2 }\)
• C) \(f ^ { - 1 } ( x ) = \sqrt { x + 2 }\)
• D) \(f ^ { - 1 } ( x ) = \sqrt { x - 2 }\)
• E)f ^-1(x) = x² + 2

Calculate marginal and total utility from given data.

Understand and apply the concept of consumer surplus.

Explain the law of diminishing marginal utility.

Interpret demand and utility data to determine consumer surplus changes with price variations.

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Definitions:

Price

The amount of money required to purchase a good or service, often determined by factors such as supply and demand.

Perfectly Competitive Firm

A company that operates in a market where there are many buyers and sellers, the product is homogeneous, and there are no barriers to entry or exit.

Normal Profit

Normal profit occurs when a firm's total revenue is equal to its total costs, including the opportunity costs of capital, providing no incentive for entry or exit in the industry.

Yearly Licensing Fee

An annual charge paid to obtain the rights to use a particular piece of intellectual property, software, or other specific products/services.