Question

The range of the function $f$ defined as $f\left(x\right)=\frac{2x}{x^2+1}$ is

• A. $[-1,1]$
• B. $[-\frac{1}{2},\frac{1}{2}]$
• C. $[-2,2]$
• D. $[0,1]$

Answer 1

The correct option is A $[-1,1]$

$y=\frac{2x}{x^2+1}$

$\Rightarrow y{x}^2+y-2x=0$

$\Rightarrow y{x}^2-2x+y=0$

As $x\in R$

$\therefore \Delta \ge 0$

$\Rightarrow 4-4y^2\ge 0$

$\Rightarrow y^2\le 1$

$\therefore y\in [-1,1]$