The minimum and maximum of the function f (x) = 3 / x, X ∈ [- 1,2] are

The minimum and maximum of the function f (x) = 3 / x, X ∈ [- 1,2] are

Incorrect domain; should be: X ∈ [- 1,0) ∪ (0,2]
F (x) is a decreasing function in the left half and right half. The whole function has neither maximum nor minimum, but extreme value and minimum value,
F (max) = f (- 1) = - 3
F (min) = f (2) = 3 / 2

If f (a) + F (A-1) > 0, find the range of A

F (a) is greater than - f (A-1) because of odd function
=F (a) is greater than f (1-A)
So the subtraction function
A is less than 1-A
At the same time to meet the domain, so - 1 is less than or equal to a, less than 1 / 2

Let f (x) be an increasing function in the domain (0, + ∞), and f (x / y) = f (x) - f (y)
If f (2) = 1, solve the inequality f (x) - f [1 / (x-3)] ≤ 2

F (1 / 1) = f (1) - f (1), so f (1) = 0, f (x) - f [1 / (x-3)] = f (x) - f (1) + F (x-3), so f (x) - f [1 / (x-3)] ≤ 2 is equivalent to f (x) - f (1) + F (x-3) ≤ f (2) + F (2) to simplify f (x) - f (2) ≤ f (2) - f (x-3), then f (x / 2) ≤ f (2 / x-3), because f (x) is an increasing function in the domain of definition (0, + ∞), so x / 2 ≤ 2 / x-3, because x > 3