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1. relation and function — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths1. relation and function1 Mark
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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