Determine I) the Domain of the Function, Ii) the Range $$f ( x ) = \frac { 4 } { 6 x + 5 }$$

question 346

Multiple Choice

Determine i) the domain of the function, ii) the range of the function, iii) the domain of the inverse, and iv) the range of
the inverse.
- $$f ( x ) = \frac { 4 } { 6 x + 5 }$$

• A) \(f ( x ) : D = \left\{ x \mid x \neq \frac { 2 } { 3 } \right\} , R = \left\{ y \mid y \neq \frac { 4 } { 5 } \right\}\);
• \(f ^ { - 1 } ( x ) : D = \left\{ x \mid x \neq \frac { 4 } { 5 } \right\} , R = \left\{ y \mid y \neq \frac { 2 } { 3 } \right\}\)
• B) \(f ( x ) : D = \left\{ x \mid x \neq \frac { 5 } { 6 } \right\} R = \{ y \mid y \neq - 5 \}\);
• \(\mathrm { f } ^ { - 1 } ( \mathrm { x } ) : \mathrm { D } = \left\{ \mathrm { x } | \mathrm { x } \neq - 5 \rangle , R = \left\{ \mathrm { y } \mid \mathrm { y } \neq \frac { 5 } { 6 } \right\} \right.\)
• C) \(f ( x )\) : \(D\) is all real numbers, \(R\) is all real number:
• \(\mathrm { f } ^ { - 1 } ( \mathrm { x } )\) : \(\mathrm { D }\) is all real numbers, \(R\) is all real numbe
• D) \(f ( x ) : D = \left\{ x \mid x \neq - \frac { 5 } { 6 } \right\} , R = \{ y \mid y \neq 0 \}\)
• \[\mathrm { f } ^ { - 1 } ( \mathrm { x } ) : \mathrm { D } = \{ \mathrm { x } \mid \mathrm { x } \neq 0 \} , \mathrm { R } = \left\{ \mathrm { y } \mid \mathrm { y } \neq - \frac { 5 } { 6 } \right\}\] ;

---

Definitions:

Globalization

The process by which businesses or other organizations develop international influence or start operating on an international scale, leading to an increase in global connections.

Governments

Institutions or groups of people governing a community or unit, making and enforcing rules for a society.

International Trade Agreements

Formal accords between countries that govern the rules, regulations, and standards for trade and economic exchange across borders.

Decreased Autonomy

A reduction in the ability or opportunity to make independent decisions or choices, often due to external control or influence.