Given the function f (x) = (2ax-1) / (2x + 1) (1) a = 1, the monotone interval (2) f (x) of F X is the range of increasing function to find a in (negative infinity, - 1 / 2)

Given the function f (x) = (2ax-1) / (2x + 1) (1) a = 1, the monotone interval (2) f (x) of F X is the range of increasing function to find a in (negative infinity, - 1 / 2)

(1) When a = 1,
f(x)=(2x-1)/(2x+1)
=[(2x+1)-2]/(2x+1)
=1-2/(2x+1)
=1-1/(x+1/2)
Move the function y = - 1 / X image 1 / 2 unit to the left, and then to the right
The image of F (x) can be obtained by moving up one unit
∵ y = - 1 / X is an increasing function on (- ∞, 0), (0, + ∞)
The monotone interval of F (x) is (- ∞, - 1 / 2), (- 1 / 2, + ∞)
In each interval, the function is an increasing function
（2）
f(x)=(2ax-1)/(2x+1)
=[a(2x+1)-(a+1)]/(2x+1)
=a-(a+1)/(2x+1）
∵ f (x) is an increasing function at (negative infinity, - 1 / 2)
∴-(a+1)0
The range of a is a > - 1