which statement is true about the function $f(x)=-sqrt{-x}$?\nthe domain of the function is all negative…

which statement is true about the function $f(x)=-sqrt{-x}$?\nthe domain of the function is all negative real numbers.\nthe range of the function is all positive real numbers.\nthe domain and range of the function have opposite signs.\nthe domain and range of the function are the same.

which statement is true about the function $f(x)=-sqrt{-x}$?\nthe domain of the function is all negative real numbers.\nthe range of the function is all positive real numbers.\nthe domain and range of the function have opposite signs.\nthe domain and range of the function are the same.

Answer

Answer:

The domain and range of the function are the same.

Explanation:

Step1: Find the domain

For $y =-\sqrt{-x}$, the expression under the square - root must be non - negative, i.e., $-x\geq0$, so $x\leq0$. The domain is ${x\in R|x\leq0}$.

Step2: Find the range

Let $t=-x$, then $y =-\sqrt{t}$ where $t\geq0$. Since $\sqrt{t}\geq0$, then $y =-\sqrt{t}\leq0$. The range is ${y\in R|y\leq0}$.

Step3: Compare domain and range

The domain is all non - positive real numbers and the range is all non - positive real numbers. So the domain and range of the function are the same.