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Let \( f:(1,3) \rightarrow R \) be a function defined by \( f(x)=\frac{x[x]}{1+x^{2}} \), where \(\left[x\right]\) denot…

Q1

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

[JEE Main 2020, 8 Jan (Shift 2)]

a

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

b

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

c

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

d

\( \left(\frac{2}{5}, \frac{4}{5}\right] \)

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