The Function F Is One-To-One $$f ( x ) = \sqrt { 5 x - 1 }$$

question 21

Multiple Choice

The function f is one-to-one. State the domain and the range of f and f^-1. Write the domain and range in set-builder
notation.
- $$f ( x ) = \sqrt { 5 x - 1 }$$

• A) \(f ( x ) : D = \{ x \mid x \geq 0 \} , R = \{ y \mid y \geq 0 \}\);
• B) \(f ( x ) : D = \left\{ x \mid x \geq \frac { 1 } { 5 } \right\} , R = \{ y \mid y \geq 0 \}\);
• \(\mathrm { f } ^ { - 1 } ( \mathrm { x } ) : \mathrm { D }\) is all real numbers, \(R = \left\{ \mathrm { y } \mid \mathrm { y } \geq \frac { 1 } { 5 } \right\}\)
• C) \(f ( x ) : D = \left\{ x \mid x \geq \frac { 1 } { 5 } \right\} , R = \{ y | y \geq 0 \rangle\);
• \(\mathrm { f } ^ { - 1 } ( \mathrm { x } ) : \mathrm { D } = \{ \mathrm { x } \mid \mathrm { x } \geq 0 \} , \mathrm { R } = \left\{ \mathrm { y } \mid \mathrm { y } \geq \frac { 1 } { 5 } \right\}\)
• D) \(f ( x ) : D = \left\{ x \mid x \geq \frac { 1 } { 5 } \right\} , R\) is all real numbers; \(f ^ { - 1 } ( x ) : D = \left\{ x | x \geq 0 \rangle , R = \left\{ y \mid y \geq \frac { 1 } { 5 } \right\} \right.\)
• \(f ^ { - 1 } ( x ) : D\) is all real numbers, \(R = \left\{ y \mid y \geq \frac { 1 } { 5 } \right\}\)

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Definitions:

Superordinate Goal

A shared goal that cannot be achieved by any one group alone and requires cooperative effort, often used to reduce conflict between groups by emphasizing common interests.

Level Of Cooperation

The extent to which individuals or groups within an organization or community are willing to work together towards common goals or interests.

One Leader

A leadership style or situation where a single individual exercises authority and makes decisions for a group or organization.

Team

A group of individuals working together towards a common goal, leveraging various skills, experiences, and perspectives for collective success.