The idea of the first question F 1(X) has a maximum value on (1, positive infinity), which is an extreme value, that is, there is inequality A-0.5 verified according to the meaning of the question. 0 。 So it is enough to find the maximum and minimum extreme values of two functions and list the inequalities about a.

In the second question, after the value of a is brought in, the extreme values of two specific functions are obtained, which shows that the maximum value of F 1(X) is less than the minimum value of F2(X).