Assertion: The domain of the function f ( x ) = 1 | x | - x is ( - , 0 ) . Reason: If | x | x , then x 0 .

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Solution

Q.
Assertion: The domain of the function $f (x)$ $= \frac{1}{\sqrt{| x | - x}}$ is $(- \infty, 0)$ .

Reason: If $| x |$ $> x$ , then $x < 0$ .

1 Both assertion and reason are true and reason is the correct explanation of assertion.

2 Both assertion and reason are true but reason is not the correct explanation of assertion.

3 Assertion is true but reason is false.

4 Assertion is false but reason is true.

Ans.
(1)

$f (x)$ $= \frac{1}{\sqrt{| x | - x}}$

$f is defined when$ $| x |$ $- x > 0 \Rightarrow$ $| x |$ $> x$

$Thus x must be negative.$

$∴$ $x \in (- \infty, 0)$

$∴$ $Both assertion and reason are true and reason is the correct explanation of assertion.$

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