Match the following
Here [ ] represents Greatest integer Function
Column-I Column-II
A) Odd function P) $x - [x] \forall x \in R$
B) Even function Q) $\log (x + \sqrt{1 + x^{2}}) \forall x \in R$
C) Neither even nor odd R) $x \log (\frac{1 + x}{1 - x}) \forall x \in (- 1, 1)$
D) Periodic function S) $\frac{2^{x / 2}}{1 + 2^{x / 2}} \forall x \in R$

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$A - S, B - P, C - P S, D - R$

$A - Q, B - R, C - P, D - R$

$A - Q, B - P, C - P, D - P$

$A - Q, B - R, C - P S, D - P$

answer is A.

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Detailed Solution

$x - [x]$ is neither even nor odd function. It is a periodic function with period ‘1’

$\log (x + \sqrt{1 + x^{2}})$ is odd function

$x \log (\frac{1 + x}{1 - x}),$ is even functions

$\frac{2^{x / 2}}{1 + 2^{x / 2}} \forall x \in R$ is neither even nor odd function

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