Find $g \circ f$ And the Domain of the Composite Function $f ( x ) = \frac { 1 } { x } , g ( x ) = x + 5$

question 12

Multiple Choice

Find $g \circ f$ and the domain of the composite function.
$f ( x ) = \frac { 1 } { x } , g ( x ) = x + 5$

• A) \(\frac { 1 } { x + 5 }\) Domain of \(g \circ f\) : all real numbers x except \(x = - 5\)
• B) \(\frac { 1 } { x } - 5\) Domain of \(g \circ f\) : all real numbers x except \(x = 0\)
• C) \(\frac { 1 } { x } + 5\) Domain of \(g \circ f\) : all real numbers x except \(x = 0\)
• D) \(- \frac { 1 } { x + 5 }\) Domain of \(g \circ f\) : all real numbers x except \(x = - 3\)
• E) \(\frac { 1 } { x - 5 }\) Domain of \(g \circ f\) : all real numbers x except \(x = 5\)

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Definitions:

EMV

Expected Monetary Value, a statistical concept used in decision making to calculate the average outcome when the future includes scenarios that may or may not happen.

Maximax Criterion

A decision rule used under uncertainty, selecting the option with the maximum possible return, focusing on the most optimistic outcome.

Row Maximums

The highest values within each row of a matrix or table, typically used in data analysis and optimization problems.

Equally Likely Criterion

A decision-making principle where all outcomes are considered to have the same probability of occurring.