Embibe Experts Solutions for Chapter: Relations and Functions, Exercise 1: Bihar Board-2020

If $A=\{1,2,3\},B=\{6,7,8\}$ and $f:A\to B$ is a function such that $f\left(x\right)=x+5$ then what type of a function is $f$?

The operation $*$ is defined as $a*b=2a+b, \mathrm{then} (2*3)*4$ is 

If $f\left(x_1\right)=f\left(x_2\right)\Rightarrow x_1=x_{2 }\mathrm{\forall }{x}_1,x_2\in A$, then what type of function is $f:A\to B$?

$f:A\to B$ will be an onto function of

If $f:R\to R$ such that $f\left(x\right)={\left(3-x^3\right)}^{\frac{1}{3}}$, then prove that $\left(f\circ f\right)\left(x\right)=x$.

The operation $*$ is defined as $a * b=3 a+4b-2$ then $4*5$.

Let $R$ be the relation in the set $\mathrm{N}$ given by 

$R=\left\{\left(a, b\right):a=b-2, b>6\right\}$

Find $gof$ and $fog$ if $f\left(x\right)=8x^3$ and $g\left(x\right)=x^{\frac{1}{3}}.$