Test Index

Functions Part 1

Section: Mathematics

Question : 43 of 100

Marks: +1, -0

f(x)=\frac{\csc^{-1} x}{\sqrt{x-\lfloor x \rfloor}}

\lfloor x \rfloor

x

x

Solution:

Given,

f(x)=\frac{\csc^{-1} x}{\sqrt{x-\lfloor x \rfloor}}

\Rightarrow \;\; f(x)=\frac{\csc^{-1} x}{\sqrt{\{x\}}}

For

f(x)

to be defined,

\left\{ \begin{array}{l} |x| \geq 1 \\ \{x\} > 0 \end{array} \right.

\Rightarrow \left\{ \begin{array}{l} x \leq -1 \; \text{ or } \; x \geq 1 \\ x \neq 1 \; \text{ integers } . \end{array} \right.

i.e.

x \in (-\infty, -1] \cup [1, \infty) - \{

integers

i.e. all non-integers except the interval

[-1,1]

(here,

-1

and 1 are included in except case, because of

-1

and 1 are integers).

Go to Question:

Prev Question

Next Question