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

question 89

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.
- $f ( x ) = \sqrt { 5 x + 4 }$

• A) \[
• f(x): D=\left\{x \mid x \geq-\frac{4}{5}\right\}, R=\{y \mid y \geq 0\}
• \]
• \( f^{-1}(x): D \) is all real numbers, \( R=\left\{y \mid y \geq-\frac{4}{5}\right\} \)
• B) \(f ( x ) : D = \left\{ x \mid x \geq - \frac { 4 } { 5 } \right\} , R = \{ y \mid y \geq 0 \}\); \(\mathrm { f } ^ { - 1 } ( \mathrm { x } )\) : \(\mathrm { D }\) is all real numbers, \(\mathrm { R } = \left\{ \mathrm { y } \mid \mathrm { y } \geq - \frac { 4 } { 5 } \right\}\) \(\mathrm { f } - 1 ( \mathrm { x } ) : \mathrm { D } = \left\{ \mathrm { x } | \mathrm { x } \geq 0 \rangle , \mathrm { R } = \left\{ \mathrm { y } \mid \mathrm { y } \geq - \frac { 4 } { 5 } \right\} \right.\)
• C) \(f ( x ) : D = \left\{ x \mid x \geq - \frac { 4 } { 5 } \right\} , R\) is all real numbers;
• \(f^{-1}(x): D \text { is all real numbers, } R=\left\{y \mid y \geq-\frac{4}{5}\right\}\)
• D)
• \(\begin{array}{l}
• f(x): D=\{x \mid x \geq 0\}, R=\{y \mid y \geq 0\} \\
• f^{-1}(x): D=\{x \mid x \geq 0\}, R=\left\{y \mid y \geq-\frac{4}{5}\right\}
• \end{array}\)

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Definitions:

Cumulative Preferred Stock

A type of preferred stock that entitles shareholders to receive dividends in arrears before any dividends can be distributed to common stockholders.

Par Common Stock

The nominal or face value assigned to common shares by the company's charter, which has little relation to the market value of the shares.

Stock Dividend

A dividend payment made in the form of additional shares rather than a cash payout.

Retained Earnings

Profits that are held back in a company to be reinvested in its operations or to pay down debt rather than being distributed to shareholders as dividends.