Use Function Notation to Write $g$ In Terms Of $f ( x ) = x ^ { 3 }$

question 25

Multiple Choice

Use function notation to write $g$ in terms of $f ( x ) = x ^ { 3 }$ .
$$g ( x ) = - \frac { 1 } { 5 } ( x + 4 ) ^ { 3 }$$

• A) \(\quad g ( x ) = - \frac { 1 } { 5 } [ f ( x ) ] ^ { 3 } + 4\)
• B) \(g ( x ) = - \frac { 1 } { 5 } [ f ( x ) + 4 ]\)
• C) \(g ( x ) = - [ f ( x ) ] ^ { 3 } + \frac { 64 } { 5 }\)
• D) \(g ( x ) = - \frac { 1 } { 5 } [ f ( x ) ] ^ { 3 } + 64\)
• E) \(\quad g ( x ) = - \frac { 1 } { 5 } [ f ( x + 4 ) ]\)

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Definitions:

Universal Instantiation

A logical rule of inference that allows the derivation of a particular instance from a general statement, often used in formal proofs.

Universal Generalization

A logical rule that states if something is true for all members of a class, it is true in general.

Quantifier Negation

A logical operation that reverses the scope of a quantifier in a statement, changing its overall truth value.

Existential Generalization

A logical operation that infers the existence of at least one individual meeting a specified condition from a statement concerning that individual.