Question

What is the domain and range of `f(x)=sqrt(16-x^3)`?

Answer 1

Domain: `x <= root(3)16 or (-oo , root(3)16]`
Range: `f(x) >=0 or [0,oo)`

Explanation:

`f(x)=sqrt(16-x^3)` Domain: under root should not be negative , so
`16-x^3 >=0 or 16 >= x^3 or x^3 <= 16 or x <= root(3)16`

Domain: `x <= root(3)16 or (-oo , root(3)16]`

Range: `f(x)` is any real value `>=0`

Range: `f(x) >=0 or [0,oo)`
graph{(16-x^3)^0.5 [-10, 10, -5, 5]}