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

question 193

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

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

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