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Maths-

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Question

$text If end text f left parenthesis x right parenthesis equals fraction numerator 1 over denominator square root of vertical line x vertical line minus x end root end fraction text then, domain of end text f left parenthesis x right parenthesis text is end text$

$(- \infty, 0)$
$(- \infty, 1)$
$(- \infty, \infty)$
None of the above

The correct answer is: $left parenthesis negative straight infinity comma 0 right parenthesis$

$f left parenthesis x right parenthesis$ is defined
When $vertical line x vertical line greater than x$
$not stretchy rightwards double arrow space of 1em x less than negative x comma x greater than x$
$not stretchy rightwards double arrow 2 x less than 0 comma left parenthesis x greater than x text is not possible end text right parenthesis$
$not stretchy rightwards double arrow space of 1em x less than 0$
Hence domain of $f left parenthesis x right parenthesis text is end text left parenthesis negative straight infinity comma 0 right parenthesis$

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