The Function F Is One-To-One $$f ( x ) = x ^ { 2 } + 1 , x \geq 0$$

question 144

Multiple Choice

The function f is one-to-one. Find its inverse.
- $$f ( x ) = x ^ { 2 } + 1 , x \geq 0$$

• A) \(\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \sqrt { \mathrm { x } } - 1 , \mathrm { x } \geq 0\)
• B) \(f ^ { - 1 } ( x ) = \sqrt { x - 1 } , x \geq 1\)
• C) \(\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \sqrt { \mathrm { x } + 1 } , \mathrm { x } \geq - 1\)
• D) \(\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \sqrt { \mathrm { x } } - 1 , \mathrm { x } < 0\)

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Definitions:

Short-Run Average Total Cost (ATC)

The total cost per unit of output in the short run, where some factors of production are fixed.

Profit-Maximizing Level

The output level at which a firm achieves the highest profit, where marginal revenue equals marginal cost.

Average Total Costs (ATC)

A rephrasing of Average Total Cost, it calculates the per-unit production cost by dividing the total cost by the total quantity of goods produced.

Manufacturing Firm

A business that uses components, parts, or raw materials to make a finished good.