For the Given Functions F and G, Find the Requested $$f ( x ) = 2 x ^ { 3 } - 1 ; g ( x ) = 5 x ^ { 2 } + 2$$

question 239

Multiple Choice

For the given functions f and g, find the requested function and state its domain.
- $$f ( x ) = 2 x ^ { 3 } - 1 ; g ( x ) = 5 x ^ { 2 } + 2$$
Find $f \cdot g$ .

• A) \(( \mathrm { f } \cdot \mathrm { g } ) ( \mathrm { x } ) = 10 \mathrm { x } ^ { 5 } + 4 \mathrm { x } ^ { 3 } - 5 \mathrm { x } ^ { 2 } - 2\); all real numbers
• B) \(( f \cdot g ) ( x ) = 10 x ^ { 6 } + 4 x ^ { 3 } - 5 x ^ { 2 } - 2\); all real numbers
• C) \(( \mathrm { f } \cdot \mathrm { g } ) ( \mathrm { x } ) = 2 \mathrm { x } ^ { 3 } + 5 \mathrm { x } ^ { 2 } - 2 ;\) all real numbers
• D) \(( f \cdot g ) ( x ) = 10 x ^ { 5 } + 4 x ^ { 3 } - 5 x ^ { 2 } - 2 ; \{ x \mid x \neq 0 \}\)

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Definitions:

Binocular Cues

Visual information taken in by two eyes that enable a sense of depth perception, such as stereopsis, convergence, and parallax.

3D Movies

Films that create the illusion of depth perception, typically using special glasses, to enhance the viewing experience.

Principle

A fundamental truth or proposition that serves as the foundation for a system of belief, behavior, or reasoning.

Pictorial Depth Cues

Visual indicators that can create the illusion of depth in two-dimensional representations, aiding in the perception of three-dimensionality.