The set of values of x for which 1-x-x- is defined- is A- 0- -B- R -0C- RD- -0- -

The correct option is A (0,∞)1√(x+|x|) is defined when x+|x| 0 So x 0 When x 0 x+|x| 0 ⇒ 2x 0 ⇒ x 0 When x 0 x+|x| 0 ⇒ x x 0 ⇒ 0 0 Not possible. Henc ...

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Standard XII

Mathematics

Absolute Value Function

The set of va...

Question

The set of values of $x$ for which $\frac{1}{\sqrt{x + | x |}}$ is defined, is

(0, \infty)

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[0, \infty)

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R

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R - {0}

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Solution

The correct option is A $(0, \infty)$
$\frac{1}{\sqrt{x + | x |}}$ is defined when

$x + | x | > 0$
So $x \neq 0$

When $x > 0$
$x + | x | > 0$
$\Rightarrow 2 x > 0 \Rightarrow x > 0$

When $x < 0$
$x + | x | > 0 \Rightarrow x - x > 0 \Rightarrow 0 > 0$
Not possible.

Hence, $x \in (0, \infty)$

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The set of values of x for which 1√x+|x| is defined, is

The correct option is A (0,∞)1√x+|x| is defined when x+|x|>0 So x≠0 When x>0 x+|x|>0 ⇒2x>0⇒x>0 When x<0 x+|x|>0⇒x−x>0⇒0>0 Not possible. Hence, x∈(0,∞)

The set of values of $x$ for which $\frac{1}{\sqrt{x + | x |}}$ is defined, is

The correct option is A $(0, \infty)$
$\frac{1}{\sqrt{x + | x |}}$ is defined when

$x + | x | > 0$
So $x \neq 0$

When $x > 0$
$x + | x | > 0$
$\Rightarrow 2 x > 0 \Rightarrow x > 0$

When $x < 0$
$x + | x | > 0 \Rightarrow x - x > 0 \Rightarrow 0 > 0$
Not possible.

Hence, $x \in (0, \infty)$