Answer:
It has the same domain as the function ![f(x)=-\sqrt{-x}](https://tex.z-dn.net/?f=f%28x%29%3D-%5Csqrt%7B-x%7D)
Step-by-step explanation:
we have
![f(x)=\sqrt{-x}](https://tex.z-dn.net/?f=f%28x%29%3D%5Csqrt%7B-x%7D)
we know that
The radicand cannot be a negative number
so
![-x\geq 0](https://tex.z-dn.net/?f=-x%5Cgeq%200)
Solve for x
Multiply by -1 both sides
![x\leq 0](https://tex.z-dn.net/?f=x%5Cleq%200)
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
<u><em>Verify each statement</em></u>
Part 1) It has the same domain as the function ![f(x)=-\sqrt{-x}](https://tex.z-dn.net/?f=f%28x%29%3D-%5Csqrt%7B-x%7D)
<em>The statement is true</em>
The domain of the function
is
the interval ---> (-∞,0]
Part 2) It has the same range as the function ![f(x)=-\sqrt{-x}](https://tex.z-dn.net/?f=f%28x%29%3D-%5Csqrt%7B-x%7D)
The statement is false
The range of the function
is
the interval ---> (-∞,0]
Part 3) It has the same domain as the function ![f(x)=-\sqrt{x}](https://tex.z-dn.net/?f=f%28x%29%3D-%5Csqrt%7Bx%7D)
The statement is false
The domain of the function
is
the interval ---> [0,∞)
Part 4) It has the same range as the function ![f(x)=-\sqrt{x}](https://tex.z-dn.net/?f=f%28x%29%3D-%5Csqrt%7Bx%7D)
The statement is false
The range of the function
is
the interval ---> (-∞,0]