R D Sharma Solutions for Chapter: Function, Exercise 1: MULTIPLE CHOICE QUESTIONS (MCQs)

If $\mathrm{f}:\mathrm{A}\to \mathrm{B}$ given by $3^{\mathrm{f}\left(\mathrm{x}\right)}+2^{-\mathrm{x}}=4$ is a bijection, then

Let  $f\left(x\right)=\frac{1}{1-x}$. Then $\left\{fo\right(fof\left)\right\}\left(x\right)$

Let $g\left(x\right)=1+x-\left[x\right]$ and $f\left(x\right)=\left\{\begin{array}{rr}-1,& x<0\\ 0,& x=0\\ 1,& x>0\end{array}\right.$where $\left[x\right]$ denotes the greatest integer less than or equal to $x$. Then for all $x, f\left(g\right(x\left)\right)$ is equal to

If $f:R\to (-1,1)$ is defined by $f\left(x\right)=\frac{-x\left|x\right|}{1+x^2},$ then $f^{-1}\left(x\right)$ equals

Let $\left[x\right]$ denote the greatest integer less than or equal to $x$. If $f\left(x\right)={\sin }^{-1}x, g\left(x\right)=\left[x^2\right] \mathrm{and} h\left(x\right)=2x, \frac{1}{2}\le x\le \frac{1}{\sqrt{2}}$, then 

If $f\left(x\right)={\sin }^{2}x$ and the composite function $g\left(f\right(x\left)\right)=\left|\sin x\right|,$ then $g\left(x\right)$ is equal to

Let $f:R\to R$ be given by $f\left(x\right)=\tan x$. Then, $f^{-1}\left(1\right)$ is

Let $f:R-\left\{\frac{3}{5}\right\}\to R$ be defined by $f\left(x\right)=\frac{3x+2}{5x-3}$. Then,