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 nbsp; Which is not possible. When x≥0, we get x x ...

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Standard XIII

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 A $ϕ$
Let $f (x) = \frac{1}{\sqrt{x - | x |}}$
For $f$ to be defined,
$x - | x | > 0$

When $x < 0$ , we get
$x - (- x) > 0 \Rightarrow 2 x > 0 \Rightarrow x > 0$
Which is not possible.

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

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The domain of the function 1√x−|x| is

The correct option is A ϕLet 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 Which is not possible. When x≥0, we get x−x>0⇒0>0 Which is not possible. ∴D(f)=ϕ

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