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

question 51

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 \(x = 5\)

---

Definitions:

Mood Disorders

A category of mental disorders involving persistent disturbances in mood, such as depression or bipolar disorder.

Major Depressive Disorder

A psychiatric disorder characterized by persistent feelings of sadness, lack of interest in activities, and possible physical symptoms, impacting daily functioning.

Intense Feelings

Strong emotional states or reactions that can be overwhelming and deeply affect an individual's mood and behavior.

Sadness

A mental condition marked by sensations of sorrow, loss, or a lack of optimism.