Embibe Experts Solutions for Chapter: Functions, Exercise 2: Exercise-2

Identify the statement(s) which is/are incorrect ? 

If $F\left(x\right)=\frac{\mathrm{sin\pi }\left[x\right]}{\left\{x\right\}},$ then $F\left(x\right)$ is: (where $\left\{.\right\}$ denotes fractional part function and $\left[.\right]$ denotes the greatest integer function and $sgn\left(x\right)$ is a signum function)

Let $f:R\to R$ and $g:R\to R$ be two one-one and onto functions such that they are mirror images of each other about the line $y=a$. If $h\left(x\right)=f\left(x\right)+g\left(x\right),$ then $h\left(x\right)$ is

Which of following pairs of functions are identical.

For the function $\mathrm{f}\left(\mathrm{x}\right)=\ln \left({\sin }^{-1}{\log }_2\left(x\right)\right)$

Which among the following functions defined from $\left[-1,1\right]$  to $\left[-1,1\right],$ are not bijective ?

Find number of all such functions $y=f\left(x\right)$ which are one-one? 

Find the number of all such functions $y=f\left(x\right)$ which are onto