For the pair of functions, find the indicated domain.
- f(x)=2 x-5 , $g ( x ) = \sqrt { x + 6 }$
Find the domain of $\mathrm { f } \circ \mathrm { g } \text {. }$
A) (-6,6)
B) $[ - 6 , \infty )$
C) $[ 0 , \infty )$
D) $[ 6 , \infty )$

Question

For the pair of functions, find the indicated domain.
- f(x)=2 x-5 , $g ( x ) = \sqrt { x + 6 }$
Find the domain of $\mathrm { f } \circ \mathrm { g } \text {. }$
A)  (-6,6) 
B) $[ - 6 , \infty )$
C) $[ 0 , \infty )$
D) $[ 6 , \infty )$

Quizplus · Accepted Answer

The domain of $g(x) = \sqrt{x + 6}$ is $[ -6, \infty )$ because the expression inside the square root must be greater than or equal to 0. When composing $f$ with $g$, $f(g(x)) = 2\sqrt{x + 6} - 5$, the domain is determined by $g(x)$, since $f(x)$ can take any real number as input. Therefore, the domain of $f \circ g$ is $[ -6, \infty )$.

For the Pair of Functions, Find the Indicated Domain g(x)=x+6g ( x ) = \sqrt { x + 6 }g(x)=x+6​

For the Pair of Functions, Find the Indicated Domain $g ( x ) = \sqrt { x + 6 }$