Find the domain and range for the indicated function.
-$f ( x ) = \sqrt { x + 5 , } \quad g ( x ) = \sqrt { x - 5 }$
$\mathrm { f } - \mathrm { g }$
A) D: $x \geq - 5$
R: $\mathrm { y } \geq 0$

B) D: $x \geq - 5$
R: $\mathrm { y } \geq \sqrt { 10 }$

C) D: $x \geq 5$
R: $y \geq \sqrt { 10 }$

D) D: $x \geq 5$
R: $y \geq 0$

Question

Find the domain and range for the indicated function.
-$f ( x ) = \sqrt { x + 5 , } \quad g ( x ) = \sqrt { x - 5 }$
$\mathrm { f } - \mathrm { g }$
A) D: $x \geq - 5$
R: $\mathrm { y } \geq 0$

B) D: $x \geq - 5$
R: $\mathrm { y } \geq \sqrt { 10 }$

C) D: $x \geq 5$
R: $y \geq \sqrt { 10 }$

D) D: $x \geq 5$
R: $y \geq 0$

Quizplus · Accepted Answer

The domain of $f(x) = \sqrt{x + 5}$ is $x \geq -5$, and the domain of $g(x) = \sqrt{x - 5}$ is $x \geq 5$. For the function $f - g$, both square roots must be defined, so the domain is $x \geq 5$. The range depends on the values the function can take; since $f(x) - g(x)$ can result in values greater than or equal to $\sqrt{10}$ when $x = 5$, the correct range is $y \geq \sqrt{10}$.

Find the Domain and Range for the Indicated Function f(x)=x+5,g(x)=x−5f ( x ) = \sqrt { x + 5 , } \quad g ( x ) = \sqrt { x - 5 }f(x)=x+5,​g(x)=x−5​

Find the Domain and Range for the Indicated Function $f ( x ) = \sqrt { x + 5 , } \quad g ( x ) = \sqrt { x - 5 }$