Thread: Bijections

Prove that f(x) = (x-1/2) / (x(x-1)) is a one to one correspondence form (0,1) onto R.

Originally Posted by veronicak5678

Prove that f(x) = (x-1/2) / (x(x-1)) is a one to one correspondence form (0,1) onto R.

What have you tried?

I tried proving it is 1-1 by setting f(x) = f(y), but it didn't seem to work...

Originally Posted by veronicak5678

I tried proving it is 1-1 by setting f(x) = f(y), but it didn't seem to work...

Why didn't it seem to work?

I couldn't simplify it to get x = y

This should be easy to show by taking the derivative. If you need more details let me know.