A One-To-One Function Is Given $$f ( x ) = 4 x ^ { 3 } - 9$$

question 256

Multiple Choice

A one-to-one function is given. Write an expression for the inverse function.
- $$f ( x ) = 4 x ^ { 3 } - 9$$

• A) \(f ^ { - 1 } ( x ) = \frac { x - 9 } { 4 }\)
• B) \(f ^ { - 1 } ( x ) = \left( \frac { x + 9 } { 4 } \right) ^ { 3 }\)
• C) \(f ^ { - 1 } ( x ) = \frac { x + 9 } { 4 }\)
• D) \(f ^ { - 1 } ( x ) = \sqrt [ 3 ] { \frac { x + 9 } { 4 } }\)

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Definitions:

Monopoly Firm

A single company or entity that has exclusive control over the production and sale of a particular product or service.

Profit Increase

An rise in the difference between a business's revenues and its expenses, indicating improved financial performance.

Profit-Maximizing Output

The level of production at which a company achieves its highest profit, balancing revenue against costs.

Same Price

A situation where different goods, services, or commodities are sold for an identical amount of money.