For the Given Functions F and G, Find the Requested $$f ( x ) = \sqrt { 6 - x } ; g ( x ) = \sqrt { x - 2 }$$

question 141

Multiple Choice

For the given functions f and g, find the requested function and state its domain.
- $$f ( x ) = \sqrt { 6 - x } ; g ( x ) = \sqrt { x - 2 }$$
Find $f \cdot g$ .

• A) \(( f \cdot g ) ( x ) = \sqrt { ( 6 - x ) ( x - 2 ) } ; \{ x \mid x \neq 2 , x \neq 6 \}\)
• B) \(( f \cdot g ) ( x ) = \sqrt { ( 6 - x ) ( x - 2 ) } ; \{ x \mid 2 \leq x \leq 6 \}\)
• C) \(( f \cdot g ) ( x ) = \sqrt { ( 6 - x ) ( x - 2 ) } ; \{ x \mid x \geq 0 \}\)
• D) \(( \mathrm { f } \cdot \mathrm { g } ) ( \mathrm { x } ) = \sqrt { - \mathrm { x } ^ { 2 } - 12 } ; \{ \mathrm { x } \mid \mathrm { x } \neq 12 \}\)

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Definitions:

Proportion

A statistical measure that reflects the size of a part compared to the whole, expressed as a fraction, percentage, or ratio.

Nonconforming

Refers to items, processes, or conditions that do not meet predetermined standards or specifications.

Samples

A portion or subset of a larger group or population used in statistical analysis to represent the whole.

Standard Deviation

A measure of the amount of variation or dispersion of a set of values, indicating how spread out the values are from the mean.