Question

How do you find domain and range for `y=sqrt((4 - x²))`?

Answer 1

Refer to explanation

Explanation:

Since its a square root we have that

`4-x^2>=0=>(2-x)*(2+x)>=0` which holds for `[-2,2]` hence

`D(f)=[-2,2]`

The range is

`y=sqrt(4-x^2)=>y^2=4-x^2=>x^2=4-y^2>=0=>(2-y)(2+y)>=0`

Because `y>=0` we have that `R(f)=(0,2)`