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1.Relation and Function
medium
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
$R$
B
$R - \{ ( - 1,\;1) \cup (n|n \in Z)\} $
C
${R^ + } - (0,\;1)$
D
${R^ + } - \{ n|n \in N\} $
Solution
(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 $x \in R – \{ ( – 1,\,\,1)\,\, \cup \,\,(n\,\,|\,\,n \in Z)\} .$
Standard 12
Mathematics