Find the domain and range of `f(x)=sqrt(4-16x^(2))`.

Answer

Domain: [-1/2, 1/2], Range: [0, 2]

Explanation

`f(x)=y=sqrt(4-16x^(2))`
We must have `4-16x^(2) ge 0 implies x^(2) le 1//4`
`implies x in [-1//2,1//2]`
Hence domain is `[-1//2,1//2]`
Also, minimum value of function is 0 and maximum value 2 when `16x^(2)=4`
Hence range is `[0,2]`