QJEEM20Ma2bfd: JEE Main 2020 Mathematics - Class 11 JEEM20Ma2bfd Solution: Let ƒ : (1, 3) R be a function defined by , where [x] denotes…

Question

Verified Solution • 2025–26 Session moderate

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

A $\left( {{2 \over 5},{1 \over 2}} \right) \cup \left( {{3 \over 4},{4 \over 5}} \right]$
B $\left( {{3 \over 5},{4 \over 5}} \right)$
C $\left( {{2 \over 5},{4 \over 5}} \right]$
D $\left( {{2 \over 5},{3 \over 5}} \right] \cup \left( {{3 \over 4},{4 \over 5}} \right)$

Accepted Answer

f(x) =

{\begin{matrix} \frac{x}{x^{2} + 1}, & 1 < x < 2 \\ \frac{2 x}{x^{2} + 1}, & 2 \leq x < 3 \end{matrix}

\therefore

f(x) is decreasing function

\therefore

Range is

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

.

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