The function f(x) = ^ - 1 x x - [x] , where [.] denotes the great… - Vidyadip

MCQ

The function $f(x) = \frac{{{{\sec }^{ - 1}}x}}{{\sqrt {x - [x]} }},$ where $[.]$ denotes the greatest integer less than or equal to $x$ is defined for all $x$ belonging to

A
$R$
✓
$R - \{ ( - 1,\;1) \cup (n|n \in Z)\} $
C
${R^ + } - (0,\;1)$
D
${R^ + } - \{ n|n \in N\} $

✓

Answer

Correct option: B.

$R - \{ ( - 1,\;1) \cup (n|n \in Z)\} $

b
(b) The function ${\sec ^{ - 1}}x$ is defined for all $x \in R - ( - 1,\,\,1)$ and the function $\frac{1}{{\sqrt {x - [x]} }}$ is defined for all $x \in R - Z.$

So the given function is defined for all $x \in R - \{ ( - 1,\,\,1)\,\, \cup \,\,(n\,\,|\,\,n \in Z)\} .$

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