Find the domain and range of the function.
-$$g ( z ) = \sqrt { 1 - z ^ { 2 } }$$
A) D: $( - 1,1 )$, R: $( - 1,1 )$
B) D: $[ 0 , \infty )$, R: $( - \infty , \infty )$
C) D: $[ - 1,1 ]$, R: $[ 0,1 ]$
D) D: $( - \infty , \infty ) , R : ( 0,1 )$

Question

Quizplus · Accepted Answer

The domain of the function is the set of all values that can be plugged into the function without resulting in an error or undefined output. Here, the function is defined for all values of $z$ that make the expression under the square root non-negative. That is,
$$1-z^2\geq 0 \Rightarrow -1 \leq z\leq 1.$$
Thus, the domain of the function is $[ - 1,1 ]$.
On the other hand, the range of the function is the set of all possible output values. Since the square root function always gives a non-negative output, we have
$$0\leq \sqrt{1-z^2}\leq 1.$$
Therefore, the range of the function is $[0,1]$. Thus, the correct choice is C.

Find the Domain and Range of the Function g(z)=1−z2g ( z ) = \sqrt { 1 - z ^ { 2 } }g(z)=1−z2​

Find the Domain and Range of the Function $g ( z ) = \sqrt { 1 - z ^ { 2 } }$