Embibe Experts Solutions for Chapter: Sets, Relations and Functions, Exercise 1: MHT-CET 2020 (13-Oct Shift 1)

If $X=\left(4^n-3n-1:n\in N \right)$ and $Y=\left\{9\left(n-1\right):n\in N\right\}$, then $X\cap Y=$

If $A=\left\{x\right|x\in N,x$ is a prime number less than $12\}$ and $B=\left\{x\right|$$x\in N$ , $x$ is factor of $10\}$, then $A\cap B$$=$…

If $A=\{2,4\}, B=\{3,4,5\},$ then $(A\cap B)\times (A\cup B)=$

If $f:R\to R,$ such that $f\left(x\right)=\frac{e^x+e^{-x}}{e^x-e^{-x}},$ then $f$ is

If $\left|3x-2\right|\le \frac{1}{2}$, then the complete set of values of $x$ is

If $f\left(x\right)=3x+6,g\left(x\right)=4x+k$ and $fog\left(x\right)=gof\left(x\right)$ then $k=$

If $f:R\to R, g:R\to R$ are two functions defined by $f\left(x\right)=2x-3, g\left(x\right)=x^3+5$, then ${\left(fog\right)}^{-1}\left(x\right)=$