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JEE MATHEMATICS MCQ: FUNCTIONS

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Let f:(1, 3)→Rf:(1,\,3) \to R be a function defined by f(x)=x[x]1+x2f(x) = \frac{{x[x]}}{{1 + {x^2}}}, where [x][x] denotes the greatest integer ≤x.\le x. Then the range of ff is
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Correct option: D
(25,12)∪(35,45]\left( {\frac{2}{5},\frac{1}{2}} \right) \cup \left( {\frac{3}{5},\frac{4}{5}} \right]
Option D ((25,12)∪(35,45]\left( {\frac{2}{5},\frac{1}{2}} \right) \cup \left( {\frac{3}{5},\frac{4}{5}} \right]) is correct because it represents the range of the function f(x) considering the greatest integer function and the defined intervals.

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