Question

Let $f={(x,\frac {x^2}{1+x^2}):x∈R}$ be a function from R into R. Determine the range of f.

Answer 1

$f={(x,\frac {x^2}{1+x^2}):x∈R}$

= ${(0,0),(±0.5,\frac 15),(±1,\frac 12),(±1.5,\frac {9}{13}),(±2,\frac {4}{5}),(3,\frac {9}{10}),(4,\frac{16}{17}), ......}$

The range of f is the set of all second elements. It can be observed that all these elements are greater than or equal to 0 but less than 1.
[Denominator is greater numerator]
Thus, range of f= [0, 1]