For the Given Functions F and G, Find the Requested $f ( x ) = 5 x ^ { 3 } - 2 ; g ( x ) = 5 x ^ { 2 } + 3$

question 76

Multiple Choice

For the given functions f and g, find the requested function and state its domain.
- $f ( x ) = 5 x ^ { 3 } - 2 ; g ( x ) = 5 x ^ { 2 } + 3$
Find $f \cdot g$ .

• A) \(( f \cdot g ) ( x ) = 5 x ^ { 3 } + 5 x ^ { 2 } - 6\); all real numbers
• B) \(( f \cdot g ) ( x ) = 25 x ^ { 6 } + 15 x ^ { 3 } - 10 x ^ { 2 } - 6\); all real numbers
• C) \(( f \cdot g ) ( x ) = 25 x ^ { 5 } + 15 x ^ { 3 } - 10 x ^ { 2 } - 6\); all real numbers
• D) \(( f \cdot g ) ( x ) = 25 x ^ { 5 } + 15 x ^ { 3 } - 10 x ^ { 2 } - 6 ; \{ x \mid x \neq 0 \}\)

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Definitions:

Average Variable Cost

The total variable costs (costs that change with production volume) divided by the quantity of output produced.

Average Total Cost

The total cost of production divided by the quantity produced, representing the cost per unit of output.

Short Run

In economics, a period where at least one input, such as plant size or capital, is fixed and cannot be changed, contrasting with the long run where all inputs can vary.

Short Run

A period of time in economics during which at least one input is fixed, limiting the immediate capacity of businesses to adjust to market changes.