Let $f ( x ) = 2 \pi$ and $g ( x ) = \frac { 5 } { e + 3 }$ The domain of $g \circ f$ is

A) $( - \infty , \infty )$
B) $( - \infty , - 3 ) \cup ( - 3 , \infty )$
C) $( - \infty , 2 \pi ) \cup ( 2 \pi , \infty )$
D) $( - \infty , - 2 \pi ) \cup ( - 2 \pi , \infty )$
E) $( - \infty , e ) \cup ( e , \infty )$

Question

Let $f ( x ) = 2 \pi$ and $g ( x ) = \frac { 5 } { e + 3 }$ The domain of $g \circ f$ is

A) $( - \infty , \infty )$
B) $( - \infty , - 3 ) \cup ( - 3 , \infty )$
C) $( - \infty , 2 \pi ) \cup ( 2 \pi , \infty )$
D) $( - \infty , - 2 \pi ) \cup ( - 2 \pi , \infty )$
E) $( - \infty , e ) \cup ( e , \infty )$

Quizplus · Accepted Answer

The function $g \circ f$ means applying $g$ to the result of $f(x)$. Since $f(x) = 2\pi$ is a constant function and $g(x) = \frac{5}{e+3}$ is also a constant when evaluated at any $x$, the composition $g(f(x))$ will not depend on $x$ and thus is defined for all real numbers, making its domain $(- \infty , \infty )$.

Let f(x)=2πf ( x ) = 2 \pif(x)=2π And g(x)=5e+3g ( x ) = \frac { 5 } { e + 3 }g(x)=e+35​

Let $f ( x ) = 2 \pi$ And $g ( x ) = \frac { 5 } { e + 3 }$