good intuition, but "really small fractions" are not included in the range you are given, you are only considering x values between 0.5 and 1.5.
What is the maximum value of the function f(x)=1/x over the interval 1/2<x<3/2 (< means less than or equal to)?
The answer is 2, and that is the function evaluated at 1/2. Why is the answer not infinity (it is one of the choices)? If x is a really small fraction, wouldn't it keep going up and up?