which statement is true about the function $f(x)=sqrt{-x}$?\nit has the same domain as the function…

which statement is true about the function $f(x)=sqrt{-x}$?\nit has the same domain as the function $f(x)=-sqrt{-x}$.\nit has the same range as the function $f(x)=-sqrt{-x}$.\nit has the same domain as the function $f(x)=-sqrt{x}$.\nit has the same range as the function $f(x)=-sqrt{x}$.

which statement is true about the function $f(x)=sqrt{-x}$?\nit has the same domain as the function $f(x)=-sqrt{-x}$.\nit has the same range as the function $f(x)=-sqrt{-x}$.\nit has the same domain as the function $f(x)=-sqrt{x}$.\nit has the same range as the function $f(x)=-sqrt{x}$.

Answer

Explanation:

Step1: Find the domain of $f(x)=\sqrt{-x}$

For the square - root function $\sqrt{u}$, $u\geq0$. So for $y = \sqrt{-x}$, we have $-x\geq0$, which gives $x\leq0$. The domain is $(-\infty,0]$.

Step2: Find the range of $f(x)=\sqrt{-x}$

Since $\sqrt{-x}\geq0$, the range is $[0,\infty)$.

Step3: Analyze $f(x)=-\sqrt{-x}$

For the domain of $y = -\sqrt{-x}$, we have $-x\geq0$ (because of the square - root), so $x\leq0$. The domain is $(-\infty,0]$. The range is $(-\infty,0]$ since $-\sqrt{-x}\leq0$.

Step4: Analyze $f(x)=-\sqrt{x}$

For the domain of $y = -\sqrt{x}$, we have $x\geq0$. The domain is $[0,\infty)$. The range is $(-\infty,0]$.

Answer:

It has the same domain as the function $f(x)=-\sqrt{-x}$.