Answer:
It has the same range but not the same domain as the function [tex]f(x) = - \sqrt{-x}[/tex].
Step-by-step explanation:
Recall the domain of the function is all x values which input into the function and give an output. The outputs or y values are called the range. To find the domain and range, graph the function and look at where it is on the coordinate plane.
[tex]f(x) = \sqrt{x}[/tex] starts at (0,0) and curves upward and towards the right. Its domain is [tex]x\geq 0[/tex] and its range is [tex]y\geq 0[/tex].
[tex]f(x) = - \sqrt{x}[/tex] starts at (0,0) and curves downward to the right. Its domain is [tex]x\geq 0[/tex] still but its range is negative numbers or [tex]y\leq 0[/tex].
[tex]f(x) = - \sqrt{-x}[/tex] starts at (0,0) and curves downward to the left. Its domain is negative x values or [tex]x\leq 0[/tex] and its range is negative values or [tex]y\leq 0[/tex].
This means the two functions have the same range but different domains.
