What is the domain and range of $y = - (\sqrt{- x})$ $y = -(sqrt(-x))$ ?

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What is the domain and range of $y = - (\sqrt{- x})$ $y = -(sqrt(-x))$ ?

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Answer 1 · 2017-08-07T06:05:53

The domain and range both in interval notation are $(- \infty, 0]$ $(-oo,0]$ i.e. domain is given by $x \leq 0$ $x<=0$ and range is givren by $y \leq 0$ $y<=0$ .

Explanation:

As $y = - \sqrt{- x}$ $y=-sqrt(-x)$ , it is apparent that you cannot have square root of a negative number.

Hence $- x \geq 0$ $-x>=0$ or in other words $x \leq 0$ $x<=0$ - which is the domain of $x$ $x$ and in interval notation it is $(- \infty, 0]$ $(-oo,0]$ .

Now given $x \leq 0$ $x<=0$ , the range of values that $y$ $y$ can have is $(- \infty, 0]$ $(-oo,0]$ and hence range is $y \leq 0$ $y<=0$

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What is the domain and range of $y = - (\sqrt{- x})$ $y = -(sqrt(-x))$ ?

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