JEE Main 2026 (Online) 28th January Evening ShiftQuestion 1
Given below are two statements :
Statement I : The function $f:\mathbf{R}\to\mathbf{R}$ defined by $f(x)=\frac{x}{1+|x|}$ is one-one.
Statement II : The function $f:\mathbf{R}\to\mathbf{R}$ defined by $f(x)=\frac{x^2+4x-30}{x^2-8x+18}$ is many-one.
In the light of the above statements, choose the correct answer from the options given below :
Functions
Solution
$f(x)=\frac{x}{1+x}$ for $x\ge0$ and $\frac{x}{1-x}$ for $x<0$ is strictly increasing with sign preserved, so one-one. For II, $f(x)=0$ has two distinct roots $x=-2\pm\sqrt{34}$, so many-one. Both true.