Embibe Experts Solutions for Chapter: Relations and Functions, Exercise 1: Exercise

If the set $A$ contains $5$elements and the set $B$ contains $6$ elements, then the number of one-one and onto mappings from $A$ to $B$ is

Let $A=\{x:-1\le x\le 1\}$ and $f:A\to A$ such that $f\left(x\right)=x\left|x\right|$, then $f$ is

if the function $f:R\to A$ given by $f\left(x\right)=\frac{x^2}{x^2+1}$ is a surjection, then $A=$

$\mathrm{f}:\mathrm{R}\to \mathrm{R}$ given by $\mathrm{f}\left(\mathrm{x}\right)=\mathrm{x}+\sqrt{{\mathrm{x}}^2}$ is

The function $\mathrm{f}:\mathrm{R}\to \mathrm{R}$ defined by $\mathrm{f}\left(\mathrm{x}\right)=2^{\mathrm{x}}+2^{\left|\mathrm{x}\right|}$ is

Which of the following functions from $A=\{x:-1\le x\le 1\}$to itself are bijections?

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