For the Given Functions F and G, Find the Requested $f ( x ) = \sqrt { x } ; g ( x ) = 5 x - 8$

question 140

Multiple Choice

For the given functions f and g, find the requested function and state its domain.
- $f ( x ) = \sqrt { x } ; g ( x ) = 5 x - 8$
Find $\frac { \mathrm { f } } { \mathrm { g } }$ .

• A) \(\left( \frac { f } { g } \right) ( x ) = \frac { 5 x - 8 } { \sqrt { x } } ; \{ x \mid x \geq 0 \}\)
• B) \(\left( \frac { f } { g } \right) ( x ) = \frac { \sqrt { x } } { 5 x - 8 } ; \left\{ x \mid x \geq 0 , x \neq \frac { 8 } { 5 } \right\}\)
• C) \(\left( \frac { \mathrm { f } } { \mathrm { g } } \right) ( \mathrm { x } ) = \frac { \sqrt { \mathrm { x } } } { 5 \mathrm { x } - 8 } ; \left\{ \mathrm { x } \mid \mathrm { x } \neq \frac { 8 } { 5 } \right\}\)
• D) \(\left( \frac { f } { g } \right) ( x ) = \frac { \sqrt { x } } { 5 x - 8 } ; \{ x \mid x \neq 0 \}\)

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Definitions:

Ratchet Wheels

Wheels equipped with teeth that lock into place with each motion in one direction, allowing controlled movement.

Transmit Motion

The process of conveying or transferring motion from one part of a mechanical system to another.

Abbreviation

A shortened form of a word or phrase used for convenience, clarity, or brevity in written and spoken communication.

Gauge

An instrument or tool used to measure, test, or visually compare physical characteristics such as dimensions, thickness, or depth.