Mathematics - Functions Question with Solution | TestHub

Given:

$f\left(x\right)=\frac{\left[x\right]}{1+x^2}$

So,

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

Hence,

$f\left(x\right)\in \left(\frac{5}{37},\frac{2}{5}\right]$