Question

Which of the following are identical functions?
[Note : $[x]$ denotes greatest integer less than or equal to $x,\{x\}$ denotes fractional part of $x$ and $\operatorname{sgn} x$ dentoes signum function of $x$ respectively.]

• A. $f(x)=\sin ^2[\{x\}]+\cos ^2[\{x\}]$
• B. $g(x)=\operatorname{cosec}^2\{x\}-\cot ^2\{x\}$
• C. $h(x)=\operatorname{sgn}\left(\frac{x^2+1}{x^2}\right)$
• D. $k ( x )=\ln e ^{\left[\operatorname{sgn}\left( e ^{ x }+ e ^{- x }\right)\right]}$

Answer 1

Answer: (A), (D)

$ \text { For (A)}$ &$ (D) x \in R$
$\text { For (B) } x \in R-I $
$\text { For (C) } x \in R-0$
$y=1 \text { for all } $