Embibe Experts Solutions for Exercise 4: EXERCISE 2.4

If $f:R\to R$ be defined as $f\left(x\right)=2x+\left|x\right|$, then $f\left(2x\right)+f\left(-x\right)-f\left(x\right)$ is equal to

If $y=f\left(x\right)=\frac{x+2}{x-1}, x, y\ne 1$ then $x$ is equal to

Domain of function $f\left(x\right)=\ln \left\{x\right\}$, where $\left\{\right\}$ represents fractional part function.

$f\left(x\right)+f\left(1-x\right)=2$, then $f\left(\frac{1}{2}\right)$ is

Range of the $f\left(x\right)=\frac{e^x-1}{e^x+1}$

If $f\left(x\right)$ satisfies the relation $2f\left(x\right)+f\left(1-x\right)=x^2$ for all real $x$, then find $f\left(x\right)$.

Range of $f\left(x\right)=\frac{{2008}^x+{2008}^{-x}}{2}$ is ______.

Domain of ${\log }_{\left[x+1\right]}\left(x-1\right)$ is _____ $( \left[·\right]$ represents greatest integer function$)$