Functions: Let f:Rto R be defined by f(x)=fracx1+x^2 , xin R . Then the range… | JEE Main 2019 | Yukti Vault

Yukti Vault

JEE Main 2019 (Online) 11th January Morning ShiftQuestion 1

Let $f:R\to R$ be defined by $f(x)=\frac{x}{1+x^{2}}$, $x\in R$. Then the range of $f$ is

Functions

$\left[-\frac12,\frac12\right]$✓ Correct answer$R-[-1,1]$$R-\left[-\frac12,\frac12\right]$$(-1,1)-\{0\}$

Solution

$yx^2-x+y=0$ has real $x$ iff $1-4y^2\ge0$, so range is $\left[-\frac12,\frac12\right]$.

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