The function

MATHEMATICS · Single correct · AoPS · Mathematics · Special Functions · Special Functions

Problem

The function

f(x)=\frac{\sec^{-1}x}{\sqrt{x-[x]}}

, where

[\,\cdot\,]

denotes the greatest integer less than or equal to

x

, is defined for all

x

belonging to (a)

\mathbb{R}

(b)

\mathbb{R}\setminus\left((-1,1)\cup\{n\mid n\in\mathbb{Z}\}\right)

(c)

\mathbb{R}^{+}\setminus(0,1)

(d)

\mathbb{R}^{+}\setminus\{n\mid n\in\mathbb{N}\}