Answer:
![\textsf{Domain}: \quad \left[-\dfrac{1}{2}, \dfrac{1}{2}\right]](https://tex.z-dn.net/?f=%5Ctextsf%7BDomain%7D%3A%20%5Cquad%20%5Cleft%5B-%5Cdfrac%7B1%7D%7B2%7D%2C%20%5Cdfrac%7B1%7D%7B2%7D%5Cright%5D)
![\textsf{Range}: \quad [0, 1]](https://tex.z-dn.net/?f=%5Ctextsf%7BRange%7D%3A%20%5Cquad%20%5B0%2C%201%5D)
Step-by-step explanation:
Domain: set of all possible <u>input values</u> (x-values)
Range: set of all possible <u>output values</u> (y-values)
<u>Given function</u>:

As negative numbers don't have real square roots:

Therefore, to find the domain, <u>solve the inequality</u>.
Subtract 1 from both sides:

Divide both sides by -1 (reverse the inequality):

Divide both sides by 4:

![\textsf{For }\:a^n \leq b,\:\:\textsf{if }n\textsf{ is even then }-\sqrt[n]{b} \leq a \leq \sqrt[n]{b}:](https://tex.z-dn.net/?f=%5Ctextsf%7BFor%20%7D%5C%3Aa%5En%20%5Cleq%20b%2C%5C%3A%5C%3A%5Ctextsf%7Bif%20%7Dn%5Ctextsf%7B%20is%20even%20then%20%7D-%5Csqrt%5Bn%5D%7Bb%7D%20%5Cleq%20a%20%5Cleq%20%5Csqrt%5Bn%5D%7Bb%7D%3A)
![\implies -\sqrt[2]{\dfrac{1}{4}} \leq x \leq \sqrt[2]{\dfrac{1}{4}}](https://tex.z-dn.net/?f=%5Cimplies%20-%5Csqrt%5B2%5D%7B%5Cdfrac%7B1%7D%7B4%7D%7D%20%5Cleq%20x%20%5Cleq%20%5Csqrt%5B2%5D%7B%5Cdfrac%7B1%7D%7B4%7D%7D)


Therefore:
![\textsf{Domain}: \quad \left[-\dfrac{1}{2}, \dfrac{1}{2}\right]](https://tex.z-dn.net/?f=%5Ctextsf%7BDomain%7D%3A%20%5Cquad%20%5Cleft%5B-%5Cdfrac%7B1%7D%7B2%7D%2C%20%5Cdfrac%7B1%7D%7B2%7D%5Cright%5D)
To find the range, input the endpoints of the domain into the function:


To find the limit of the range, find the extreme point(s) of the function by differentiating the function and setting it to zero.



Setting it to zero and solving for x:



Substitute x = 0 into the function:

Therefore, the range is [0, 1]