Question #8cbdf

1 Answer
Sep 23, 2016

Answer:

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]}