Functions Question 17
Question 17 - 31 January - Shift 1
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
(1) $(\frac{5}{26}, \frac{2}{5}]-{\frac{9}{29}, \frac{27}{109}, \frac{18}{89}, \frac{9}{53}}$
(2) $(\frac{5}{26}, \frac{2}{5}]$
(3) $[\frac{5}{37}, \frac{2}{5}]-{\frac{9}{29}, \frac{27}{109}, \frac{18}{89}, \frac{9}{53}}$
(4) $(\frac{5}{37}, \frac{2}{5}]$
Show Answer
Answer: (4)
Solution:
Formula: Properties of Greatest Integer Function, Range of function
$f(x)=\frac{2}{1+x^{2}} \quad x \in[2,3)$
$f(x)=\frac{3}{1+x^{2}} \quad$ $x \in[3,4)$
$f(x)=\frac{4}{1+x^{2}} \quad x \in[4,5)$
$f(x)=\frac{5}{1+x^{2}} \quad x \in[5,6)$
$(\frac{5}{37}, \frac{2}{5}]$
