For any two unequal real numbers a and B, the total FA FB divided by A-B is greater than zero, then what function is FX

For any two unequal real numbers a and B, the total FA FB divided by A-B is greater than zero, then what function is FX

When FA FB and A-B are both positive, that is to say, X takes two unequal real numbers a and B (a > b), then the corresponding two function values are FA and FB. Because FA FB > 0, so FA > FB, so there is a > b, FA > FB, so it is an increasing function

If a plus B is less than or equal to zero, then FA plus FB is less than or equal to F-A plus F-B, right

Yes
a

It is known that y = f (x) decreases monotonically in (2,4) and y = f (x + 2) is an even function. Compare the sizes of F (1 / 2), f (5 / 2) and f (3)

Y = f (x + 2) is an even function
The symmetry axis of y = f (x + 2) is y-axis, that is, x = 0
If y = f (x + 2) is shifted 2 units to the right, then y = f (x)
The axis of symmetry of F (x) is x = 2
∴ f(1/2)=f(7/2)
∵ 5/2f(7/2)
That is, f (5 / 2) > F (3) > F (1 / 2)