Which pair $(s)$ of function $(s)$ is/are equal ?
where $\{x\}$ and $[x]$ denotes the fractional part $\&$ integral part functions.
Which pair $(s)$ of function $(s)$ is/are equal ?
where $\{x\}$ and $[x]$ denotes the fractional part $\&$ integral part functions.
- A
$f(x) = cos(2tan ^{ -1} x) ; g(x) =$ $\frac{{1 - {x^2}}}{{1 + {x^2}}}$
- B
$f(x) = \frac{{2x}}{{1 + {x^2}}} ; g(x) = sin(2cot ^{ -1} x)$
- C
$f(x) ={e^{\ell n(\operatorname{sgn} {{\cot }^{ - 1}}x)}} ; g(x) ={e^{\ell n\left[ {1 + \left\{ x \right\}} \right]}}$
- D
All of the above
Similar Questions
Suppose $f$ is a function satisfying $f ( x + y )= f ( x )+ f ( y )$ for all $x , y \in N$ and $f (1)=\frac{1}{5}$. If $\sum \limits_{n=1}^m \frac{f(n)}{n(n+1)(n+2)}=\frac{1}{12}$, then $m$ is equal to $...............$.
Suppose $f$ is a function satisfying $f ( x + y )= f ( x )+ f ( y )$ for all $x , y \in N$ and $f (1)=\frac{1}{5}$. If $\sum \limits_{n=1}^m \frac{f(n)}{n(n+1)(n+2)}=\frac{1}{12}$, then $m$ is equal to $...............$.
- [JEE MAIN 2023]
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