The domain of the function 1-x-x is

Let f(x)=1√(|x| x) For f to be defined, nbsp; |x| x gt;0 When x lt;0, we get x x 0 ⇒ 2x 0 ⇒ x∈ ( ∞,0) When x≥0, we get x x 0 ⇒ 0 0 Which is not possi ...

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Standard XI

Mathematics

Rational Function

The domain of...

Question

The domain of the function $\frac{1}{\sqrt{| x | - x}}$ is

ϕ

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(- \infty, 0)

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(0, \infty)

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R - {0}

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Solution

The correct option is B $(- \infty, 0)$
Let $f (x) = \frac{1}{\sqrt{| x | - x}}$
For $f$ to be defined,
$| x | - x > 0$

When $x < 0$ , we get
$- x - x > 0 \Rightarrow - 2 x > 0 \Rightarrow x \in (- \infty, 0)$

When $x \geq 0$ , we get
$x - x > 0 \Rightarrow 0 > 0$
Which is not possible.
$∴ D (f) = (- \infty, 0)$

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The domain of the function 1√|x|−x is

The correct option is B (−∞,0)Let f(x)=1√|x|−x For f to be defined, |x|−x>0 When x<0, we get −x−x>0⇒−2x>0⇒x∈(−∞,0) When x≥0, we get x−x>0⇒0>0 Which is not possible. ∴D(f)=(−∞,0)

The domain of the function $\frac{1}{\sqrt{| x | - x}}$ is