Find the domain of the composite function f∘g.
-$$f ( x ) = 4 x + 40 , \quad g ( x ) = x + 7$$
A) $( - \infty , \infty )$
B) $( - \infty , - 17 )$ or $( - 17 , \infty )$
C) $( - \infty , 17 )$ or $( 17 , \infty )$
D) $( - \infty , - 10 )$ or $( - 10 , - 7 ) ( - 7 , \infty )$

Question

Quizplus · Accepted Answer

The domain of both $f(x)$ and $g(x)$ is all real numbers $(-\infty, \infty)$ because there are no restrictions on $x$ for either function. When composing $f$ and $g$, the domain remains all real numbers.

Find the Domain of the Composite Function F∘g f(x)=4x+40,g(x)=x+7f ( x ) = 4 x + 40 , \quad g ( x ) = x + 7f(x)=4x+40,g(x)=x+7

Find the Domain of the Composite Function F∘g $f ( x ) = 4 x + 40 , \quad g ( x ) = x + 7$