Let $f:(1,3) \rightarrow \mathrm{R}$ be a function defined by
$f(\mathrm{x})=\frac{\mathrm{x}[\mathrm{x}]}{1+\mathrm{x}^{2}},$ where $[\mathrm{x}]$ denotes the greatest
integer $\leq \mathrm{x} .$ Then the range of $f$ is
Let $f:(1,3) \rightarrow \mathrm{R}$ be a function defined by
$f(\mathrm{x})=\frac{\mathrm{x}[\mathrm{x}]}{1+\mathrm{x}^{2}},$ where $[\mathrm{x}]$ denotes the greatest
integer $\leq \mathrm{x} .$ Then the range of $f$ is
- [JEE MAIN 2020]
- A
$\left(\frac{3}{5}, \frac{4}{5}\right)$
- B
$\left(\frac{2}{5}, \frac{3}{5}\right] \cup\left(\frac{3}{4}, \frac{4}{5}\right)$
- C
$\left(\frac{2}{5}, \frac{4}{5}\right]$
- D
$\left(\frac{2}{5}, \frac{1}{2}\right) \cup\left(\frac{3}{5}, \frac{4}{5}\right]$
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- [JEE MAIN 2022]
Range of $f(x) = sin^{-1} (\sqrt {x^2 + x +1})$ is -
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