MCQ
Identify the correct statement
where $[.]$ & $\{.\}$ denotes greatest integer function and fractional part function respectively.
- AIf $f(x)$ is a differentiable and increasing function then $g(x)$ = $f(f(x)) + 1$ is a decreasing function
- BIf $x \in \left( {0,1} \right)$, then $\left[ x \right]\left[ {\sin x} \right] \ne \left[ {x\sin x} \right]$
- C$f\left( x \right) = \left\{ {\cos x} \right\}\left\{ {{{\cos }^2}x} \right\}\left\{ {{{\cos }^3}x} \right\}$ is a continuous function in $\left[ {0,\frac{\pi }{2}} \right]$
- ✓$f\left( x \right) = \left\{ x \right\}\left\{ {\sin x} \right\} + \left\{ {x\sin x} \right\}$ is a differentiable function in $x \in \left( {0,1} \right)$