Question

How do you find the domain and range of `sqrt(16-x^2)`?

Answer 1

Domain : `-4 <= x <= 4`, in interval notation : `[-4,4]`
Range: `0 <= f(x) <= 4`, in interval notation : `[0,4]`

Explanation:

`f(x) = sqrt ( 16 -x^2)` , for domain under root should not be

negative quantity. `16-x^2 >= 0 or 16 >= x^2 or x^2 <=16`

`:. x <= 4 or x >=-4` . Domain : `-4 <= x <= 4 or [-4,4]`

Range : `f(x)` is maximum at `x=0 , f(x) = 4` and

`f(x)` is minimum at `x=4 , f(x) = 0`

Range : `0 <= f(x) <= 4 or [0,4]`

Domain : `-4 <= x <= 4`, in interval notation : `[-4,4]`

Range: `0 <= f(x) <= 4`, in interval notation : `[0,4]`

graph{(16-x^2)^0.5 [-10, 10, -5, 5]}