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

question 457

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

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Definitions:

Budget Constraint

The limitations on the consumption bundle that a consumer can afford given their income and the prices of goods and services.

Household's Income

The total annual income received by all members of a household, including wages, salaries, benefits, and other sources of income.

Homogeneous Products

Goods that are identical in quality and cannot be distinguished from one another by consumers.

Budget Constraint

A Budget Constraint outlines the combinations of goods and services that a consumer can purchase given their limited income and the prices of these goods and services.