Problem:
Verify that f(x) = (2x - 1)/(2x(1-x)) defines a bijection from the interval (0,1) to R (all rational numbers). (Hint: In the proof that f is surjective, use the quadratic formula).
In order for the function to be bijective it needs to be surjective and injective. I need to prove these two things. But not sure how. And I'm not sure how I'm supposed to turn that function into A,B,C components for the quadratic formula.
Any ideas?
Verify that f(x) = (2x - 1)/(2x(1-x)) defines a bijection from the interval (0,1) to R (all rational numbers). (Hint: In the proof that f is surjective, use the quadratic formula).
In order for the function to be bijective it needs to be surjective and injective. I need to prove these two things. But not sure how. And I'm not sure how I'm supposed to turn that function into A,B,C components for the quadratic formula.
Any ideas?
or do you just not pay attention during the lectures?
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