Find the domain and range of the function.
-$g ( z ) = \sqrt { 25 - z ^ { 2 } }$
A) D: (-5,5), R: (-5,5)
B)$\text { D: } [ 0 , \infty ) , \text { R: } ( - \infty , \infty )$
C) D: [-5,5], R: [0,5]
D)$\text { D: } ( - \infty , \infty ) , R : ( 0,5 )$

Question

Find the domain and range of the function.
-$g ( z ) = \sqrt { 25 - z ^ { 2 } }$
A) D: (-5,5), R: (-5,5) 
B)$\text {  D: } [ 0 , \infty ) , \text { R: } ( - \infty , \infty )$
C) D: [-5,5], R: [0,5] 
D)$\text {  D: } ( - \infty , \infty ) , R : ( 0,5 )$

Quizplus · Accepted Answer

The domain of $g(z) = \sqrt{25 - z^2}$ is determined by the condition $25 - z^2 \geq 0$, which holds for $-5 \leq z \leq 5$, so the domain is $[-5,5]$. The range is from 0 to 5, inclusive, because the square root function outputs non-negative values, and the maximum value of $g(z)$ occurs when $z = 0$, giving $\sqrt{25} = 5$. Therefore, the range is $[0,5]$.

Find the Domain and Range of the Function g(z)=25−z2g ( z ) = \sqrt { 25 - z ^ { 2 } }g(z)=25−z2​

Find the Domain and Range of the Function $g ( z ) = \sqrt { 25 - z ^ { 2 } }$