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  • The function <img alt="f\left( x \right) = \frac{{{{\sec }^{ - 1}}x}}{{\sqrt {x - [x]} }}" src="h

The function f\left( x \right) = \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 

Option: 1

R


Option: 2

( -\infty , -1] \cup [1,\infty ) - Z


Option: 3

{R^ + } - \left( {0,\,\,1} \right)


Option: 4

{R^ + } - \left\{ {n|n \in N} \right\}


Answers (1)

best_answer

The function {\sec ^{ - 1}}x is defined for its domain  x \in \left [ -\infty , -1] \cup [1,\infty \right ]

And for the function \frac{1}{{\sqrt {x - [x]} }} to be defined, x \in R - Z

So, the domain of the given function is intersection of these 2 domains, which equals ( -\infty , -1] \cup [1,\infty ) - Z

Posted by

sudhir.kumar

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