Embibe Experts Solutions for Chapter: Functions, Exercise 1: BITSAT 2017

Number of solution of the equation $\left|\cos x\right|=2\left[x\right]$ are (where $\left|x\right|,\left[x\right]$ are modulus and greatest integer function respectively).

The inverse of the function $f\left(x\right)={\log }_a\left(x+\sqrt{x^2+1}\right)$ (where, $a<0, a\ne 1$) is

Let $f:R\to R$ be a function satisfying $f\left(x+y\right)=f\left(x\right)+2y^2+kxy$ for all $x,y\in R$. If $f\left(1\right)=2$ and $f\left(2\right)=8$, then $f\left(x\right)$ is equal to

Let $A=\left[-1,1\right]$ and $f:A\to A$ be defined as $f\left(x\right)=x\left|x\right|$ for all $x\in A$, then $f\left(x\right)$ is