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 $x = 5$

Question

​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 $x = 5$

Quizplus · Accepted Answer

To find $g \circ f$, we substitute $f(x)$ into $g(x)$, resulting in $g(f(x)) = g\left(\frac{1}{x}\right) = \frac{1}{x} + 5$. The domain excludes $x = 0$ because $f(x) = \frac{1}{x}$ is undefined at $x = 0$.

​Find g∘fg \circ fg∘f And the Domain of the Composite Function f(x)=1x,g(x)=x+5f ( x ) = \frac { 1 } { x } , g ( x ) = x + 5f(x)=x1​,g(x)=x+5

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