Question

Question #8cbdf

Answer 1

Domain: `[0, oo)`

Range: `[0, oo)`

Explanation:

Assuming we are restricted to `RR` (the real numbers), the principal square root function `sqrt(*)` has a domain `[0, oo)` and a range `[0, oo)`.

No negative values are in the domain, as the square root of a negative value is an imaginary number.

(specifically, if `a>0`, then `sqrt(-a) = sqrt(a)i`)

No negative values are in the range, as the square of a negative is a positive, and the principal square root of that positive is defined as its positive real root.

We can see the domain and range clearly when examining the graph `y=sqrt(x)` by noticing that it follows the restrictions `x>=0` and `y>=0`.

graph{sqrt(x) [-10, 10, -5, 5]}