I want to show the range of y is R for all x. y=(2x-1)/(2x^2-4x+1)
I made a quadratic equation and used the fact that the discriminant >=0 for real x. It was solved to y>=0.5(i-1).
What is the meaning of ? How do you define inequalities in the complex plane?
We want to show that for , no matter what our choice of k is, there is always a real solution for x. Equation becomes
The discriminant D is
, which is positive for all real k.