Let FX be an odd function defined on [- 1,1]. For any a, B belongs to [- 1,1]. When a + B is not equal to 0, (FA + FB) / (a + b) is greater than 0. If a is greater than B, compare the size of FA and FB. Solve the inequality f (x-0.5) is less than f (the square of x-0.25)

Let FX be an odd function defined on [- 1,1]. For any a, B belongs to [- 1,1]. When a + B is not equal to 0, (FA + FB) / (a + b) is greater than 0. If a is greater than B, compare the size of FA and FB. Solve the inequality f (x-0.5) is less than f (the square of x-0.25)

F (x) is an odd function. F (x) = - f (- x) is the same as: F (b) = - f (- b). F (a) + F (b)) / (a + b) > 0. Similarly, (f (a) + f (- b)) / (a + (- b)) > 0. So, (f (a) - f (b)) / (a-b) > 0. Because a > b, f (a) > F (b)