Specify the Domain Of $( g \circ f ) ( x )$

question 107

Multiple Choice

Specify the domain of $( g \circ f ) ( x )$ for the pair of functions $f ( x ) = \frac { 3 } { 2 x } \text { and } g ( x ) = \frac { 1 } { x + 6 }$

• A) \(( - \infty , - 6 ) \cup ( - 6 , \infty )\)
• B) \(( - \infty , 0 ) \cup ( 0 , \infty )\)
• C) \(( - \infty , - 6 ) \cup ( 0 , \infty )\)
• D) \(( - \infty , - 6 ) \cup ( - 6,0 ) \cup ( 0 , \infty )\)

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Definitions:

Argument

A set of statements intended to establish a position or point of view, typically consisting of premises and a conclusion.

Explanandum

The proposition whose truth one is attempting to explain.

Diagram

A visual representation designed to illustrate the relationships between different elements of a system or process.

Premises

Statements or propositions from which a conclusion is drawn in an argument; the grounding or basis of the argument.