If the function f (x) = {(2b-1) x + B-1, x > 0, is an increasing function on R, then the value range of function B is {- X & # 178; + (2-B) x, X ≤ 0 According to the meaning of the title {2b-1 ＞ 2, ﹛2-b＞0 ﹛b-1≥f（0）, How do these three inequalities come from?

If the function f (x) = {(2b-1) x + B-1, x > 0, is an increasing function on R, then the value range of function B is {- X & # 178; + (2-B) x, X ≤ 0
According to the meaning of the title {2b-1 ＞ 2,
﹛2-b＞0
﹛b-1≥f（0）,
How do these three inequalities come from?
Analysis: ∵ piecewise function:
F(x)=(2b-1)x+b-1,(x>0)
F(x)=-x^2+(2-b)x,(x≤0)
It is an increasing function on R
When x > 0, f (x) = (2b-1) x + B-1, it will increase monotonically as long as the slope of the line is 2b-1 > 0;
When x0 = > 2-B > 0;
And ∵ is an increasing function on R
When x > 0, the intersection of F (x) = (2b-1) x + B-1 and y-axis is B-1, when x = f (0) = 0

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