Find $f \circ g$ and the domain of the composite function.
$f ( x ) = \frac { 1 } { x } , g ( x ) = x + 7$

A) $\frac { 1 } { x } + 7$ Domain of $f \circ g$ : all real numbers x except $x = 0$
B) $- \frac { 1 } { x + 7 }$ Domain of $f \circ g$ : all real numbers x except $x = - 7$
C) $\frac { 1 } { x + 7 }$ Domain of $f \circ g$ : all real numbers x except $x = - 7$
D) $\frac { 1 } { x } - 7$ Domain of $f \circ g$ : all real numbers x except $x = 0$
E) $\frac { 1 } { x - 7 }$ Domain of $f \circ g$ : all real numbers x except $x = 7$

Question

Find $f \circ g$ and the domain of the composite function. 
 $f ( x ) = \frac { 1 } { x } , g ( x ) = x + 7$

A) $\frac { 1 } { x } + 7$ Domain of $f \circ g$ : all real numbers x except $x = 0$
B) $- \frac { 1 } { x + 7 }$ Domain of $f \circ g$ : all real numbers x except $x = - 7$
C) $\frac { 1 } { x + 7 }$ Domain of $f \circ g$ : all real numbers x except $x = - 7$
D) $\frac { 1 } { x } - 7$ Domain of $f \circ g$ : all real numbers x except $x = 0$
E) $\frac { 1 } { x - 7 }$ Domain of $f \circ g$ : all real numbers x except $x = 7$

Quizplus · Accepted Answer

The composite function $f \circ g$ means applying $g$ first and then $f$, so $f(g(x)) = f(x+7) = \frac{1}{x+7}$. The domain excludes $x = -7$ to avoid division by zero.

Find f∘gf \circ gf∘g And the Domain of the Composite Function f(x)=1x,g(x)=x+7f ( x ) = \frac { 1 } { x } , g ( x ) = x + 7f(x)=x1​,g(x)=x+7

Find $f \circ g$ And the Domain of the Composite Function $f ( x ) = \frac { 1 } { x } , g ( x ) = x + 7$