Let ƒ : (1, 3) $\to$ R be a function defined by
$f(x) = {{x\left[ x \right]} \over {1 + {x^2}}}$ , where [x] denotes the greatest
integer $\le$ x. Then the range of ƒ is
Solution
f(x) = $$\left\{ {\matrix{
{{x \over {{x^2} + 1}},} & {1 < x < 2} \cr
{{{2x} \over {{x^2} + 1}},} & {2 \le x < 3} \cr
} } \right.$$
<br><br>$\therefore$ f(x) is decreasing function
<br><br>$\therefore$ Range is $$\left( {{2 \over 5},{1 \over 2}} \right) \cup \left( {{3 \over 4},{4 \over 5}} \right]$$.
About this question
Subject: Mathematics · Chapter: Sets, Relations and Functions · Topic: Sets and Operations
This question is part of PrepWiser's free JEE Main question bank. 195 more solved questions on Sets, Relations and Functions are available — start with the harder ones if your accuracy is >70%.