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

$\left( { - \infty ,\;\infty } \right)$

$\left[ { - 1,{\rm{ }}1} \right]$

$\left[ { - \sqrt 2 ,\sqrt 2 } \right]$

JEE MATHEMATICS MCQ: FUNCTIONS

1 Easy

1 of 1

Analyzing +4 | -1

Range of the function

f\left( x \right) = \frac{x}{{1 + {x^2}}}

View answer and explanation

Correct option: C

\left[ { - \frac{1}{2},\frac{1}{2}} \right]

Option C

\left[ { - \frac{1}{2},\frac{1}{2}} \right]

is correct because the range is found by solving the quadratic inequality derived from the function.