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

question 160

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

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Definitions:

Cardinal Utility Function

Utility function describing by how much one market basket is preferred to another.

Ordinal Utility Function

Utility function that generates a ranking of market baskets in order of most to least preferred.

Budget Line

A graphical representation of all possible combinations of two goods that can be purchased with a given budget and prices.

Slope

The rate at which a line or curve inclines or declines, indicating the steepness.