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## Homework Statement

f:]1,+∞[→]2,+∞[

x→ 2x/(x-1)

## Homework Equations

Prove that f is injective and serjective.

## The Attempt at a Solution

I already proved that it's injective by stating the injectivity law:

for every (a,b)ε]1,+∞[: f(a)=f(b) implies a=b

so: 2a/(a-1)=2b/(b-1) entails: 2ab-2b=2ab-2a entails -2b=-2a entails a=b

Can anyone please tell me how to prove that its serjective?