If the domain of the function f ( x )=[ x ] 1+ x ^2 , where [x] i… - Vidyadip

MCQ

If the domain of the function $f ( x )=\frac{[ x ]}{1+ x ^2}$, where $[x]$ is greatest integer $\leq x$, is $(2,6)$, then its range is

A
$\left(\frac{5}{26}, \frac{2}{5}\right]-\left\{\frac{9}{29}, \frac{27}{109}, \frac{18}{89}, \frac{9}{53}\right\}$
B
$\left(\frac{5}{26}, \frac{2}{5}\right]$
C
$\left(\frac{5}{37}, \frac{2}{5}\right]-\left\{\frac{9}{29}, \frac{27}{109}, \frac{18}{89}, \frac{9}{53}\right\}$
✓
$\left(\frac{5}{37}, \frac{2}{5}\right]$

✓

Answer

Correct option: D.

$\left(\frac{5}{37}, \frac{2}{5}\right]$

d
$\begin{array}{ll}f(x)=\frac{2}{1+x^2} & x \in[2,3) \\ f(x)=\frac{3}{1+x^2} & x \in[3,4) \\ f(x)=\frac{4}{1+x^2} & x \in[4,5) \\ f(x)=\frac{5}{1+x^2} & x \in[5,6)\end{array}$

$\left(\frac{5}{37}, \frac{2}{5}\right]$

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