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

question 491

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