Solve the Problem $$f ( x ) = x ^ { 2 } - 8 ( x \geq 0 )$$

question 12

Multiple Choice

Solve the problem.
- $$f ( x ) = x ^ { 2 } - 8 ( x \geq 0 )$$

• A) \(\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \mathrm { x } ^ { 2 } + 8 , \mathrm { x } \geq - 8\)
• B) \(f ^ { - 1 } ( x ) = \sqrt { x + 8 } , x \geq - 8\)
• C) \(\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \sqrt { \mathrm { x } - 8 } , \mathrm { x } \geq 8\)
• D) \(f ^ { - 1 } ( x ) = \sqrt { x ^ { 2 } + 8 } , x \geq - 8\)

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Definitions:

Competitive Price-searcher

A firm operating in a market where it must search for the optimal price that balances its desire for profits with the need to remain competitive.

Long-run Equilibrium

A state in which all firms in a market are making zero economic profit, leading to an optimal allocation of resources.

Competitive Price-searcher

A market participant who sets prices through active search and strategy, often in markets with some degree of product differentiation.