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High school mathematics piecewise function
If (2x-1) < = (x-1), f (x) = (2x-1) 2-(2x-1) (x-1) = 2x 2.

if(2x- 1)>; (x- 1),f(x)=(x- 1)^2-(2x- 1)(x- 1)=-x^2+3x+ 1

2x^2-x=m

-x 2+3x+ 1 = m,

2x^2-x-m=0

X 2-3x+M- 1 = 0 has three unequal real roots.

Vieta's theorem can be used to find out.