For f to be a function- the domain of f- if fx- 1 - x - -x is

The correct option is A ( ∞ ,0) Given f(x)=1√(|x| x) We know f(x) is defined if |x| x gt;0 ⇒ |x| gt;x For x gt;0,x gt;x ...

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Standard XII

Mathematics

Rational Function

For f to be...

Question

For $f$ to be a function, the domain of $f$ , if $f (x) = \frac{1}{\sqrt{| x | - x}}$ is

(- \infty, 0)

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(0, \infty)

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(- \infty, \infty)

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(- \infty, 0]

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Solution

The correct option is A $(- \infty, 0)$
Given $f (x) = \frac{1}{\sqrt{| x | - x}}$

We know $f (x)$ is defined if $| x | - x > 0$

$\Rightarrow | x | > x$

For $x > 0, x > x$ (not possible) and

For $x < 0, - x > x \Rightarrow 2 x < 0 \Rightarrow x < 0$ (possible)

Hence domain of $f$ is $(- \infty, 0)$

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For f to be a function, the domain of f, if f(x)=1√|x|−x is

The correct option is A (−∞,0)Given f(x)=1√|x|−xWe know f(x) is defined if |x|−x>0⇒|x|>xFor x>0,x>x (not possible) andFor x<0,−x>x⇒2x<0⇒x<0 (possible)Hence domain of f is (−∞,0)

For $f$ to be a function, the domain of $f$ , if $f (x) = \frac{1}{\sqrt{| x | - x}}$ is