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

question 69

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

Retina

The light-sensitive layer of tissue at the back of the inner eye that converts light images into neural signals sent to the brain.

Optic Disk

Area of the retina where the optic nerve exits the retina; lacks photoreceptors and so causes a blind spot.

Optic Pit

A small depression in the optic disc where nerve fibers exit the eye, contributing to the blind spot.

Sensory Stimulus

A detectable change in the internal or external environment that elicits a response from the sensory system.