The range of the function f(x) = x2/(1 + x2) is:

1. Analyze the expression:

   $$f(x) = \frac{x^2}{1 + x^2}$$

2. Determine the Minimum Value:

   Because x2 is a squared term, its value can never be negative for any real number x. The smallest possible value x2 can achieve is 0 (when x = 0).

   $$f(0) = \frac{0^2}{1 + 0^2} = 0$$

   Therefore, the minimum value of the function is 0, and it is inclusive (the function actually reaches 0).

3. Determine the Maximum Value:

   For any real number x, the numerator (x2) will always be exactly 1 less than the denominator (1 + x2).

   Since the numerator is strictly smaller than the denominator, the value of the fraction must always be less than 1.

   As x grows towards infinity, the +1 in the denominator becomes negligible, and the fraction approaches $1$ but never quite touches it. This means 1 is an exclusive upper bound.

Combining these insights, the exact mathematical range is [0, 1).