Question 22 - 2020 (08 Jan Shift 2)

Let $f(1, 3) \to \mathbb{R}$ be a function defined by $f(x) = \frac{x[x]}{1+x^2}$, where $[x]$ denotes the greatest integer $\le x$. Then the range of $f$ is:

(1) $\left(\frac{2}{5}, \frac{3}{5}\right) \cup \left(\frac{3}{4}, \frac{4}{5}\right)$

(2) $\left(\frac{2}{5}, \frac{1}{2}\right) \cup \left(\frac{3}{5}, \frac{4}{5}\right)$

(3) $\left(\frac{2}{5}, \frac{1}{2}\right) \cup \left(\frac{3}{4}, \frac{4}{5}\right)$

(4) $\left(\frac{2}{5}, \frac{3}{5}\right) \cup \left(\frac{3}{4}, \frac{4}{5}\right)$

Type: MCQ