Answer:
It has the same domain as the function [tex]f(x)=-\sqrt{-x}[/tex]
Step-by-step explanation:
we have
[tex]f(x)=\sqrt{-x}[/tex]
we know that
The radicand cannot be a negative number
so
[tex]-x\geq 0[/tex]
Solve for x
Multiply by -1 both sides
[tex]x\leq 0[/tex]
The domain of the given function is the interval ----> (-∞,0]
All real numbers less than or equal to 0
The range of the given function is the interval ----> [0,∞)
All real numbers greater than or equal to zero
Verify each statement
Part 1) It has the same domain as the function [tex]f(x)=-\sqrt{-x}[/tex]
The statement is true
The domain of the function [tex]f(x)=-\sqrt{-x}[/tex] is
the interval ---> (-∞,0]
Part 2) It has the same range as the function [tex]f(x)=-\sqrt{-x}[/tex]
The statement is false
The range of the function [tex]f(x)=-\sqrt{-x}[/tex] is
the interval ---> (-∞,0]
Part 3) It has the same domain as the function [tex]f(x)=-\sqrt{x}[/tex]
The statement is false
The domain of the function [tex]f(x)=-\sqrt{x}[/tex] is
the interval ---> [0,∞)
Part 4) It has the same range as the function [tex]f(x)=-\sqrt{x}[/tex]
The statement is false
The range of the function [tex]f(x)=-\sqrt{x}[/tex] is
the interval ---> (-∞,0]
