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Let f : (1, 3) \(\to\) R be a function defined by \(f(x)=\frac{x[x]}{1+{x}^{2}},\) where [ x ] denotes the greatest inte…

Q1

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

a

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

b

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

c

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

d

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

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