The first step to solving is to understand what is given and what is asked.
We are given a certain function (1/(x2+1)). We are being asked - what all values can (1/(x2+1)) take?
Whatever the value of x, x2 has to be >=0.
- If x =0, then x2 is 0
- If x is negative or positive, then x2 is positive.
So, (1/(x2+1)) is either 1 (when x =0, (1/(x2+1)) = 1/1 = 1) or a positive fraction (greater than o, lesser than 1). Example - x = -3, (1/(x2+1)) = 1 /10 = 0.1
In essence, whatever the value of x, (1/(x2+1)) has a "range" 0<x <=1 (positive, real numbers <=1). So, choice E.