# Thread: Proof that f is injective?

1. ## Proof that f is injective?

How would i go about solving this problem?

Would i start with f(x) = f(y) ?

2. Originally Posted by kensington
How would i go about solving this problem?

Would i start with f(x) = f(y) ?

Either I'm missing something or this is immediate: $x\neq y\Longrightarrow |f(x)-f(y)|=c|x-y|^\alpha > 0$ , and we're done...

Tonio

3. Yes, you can start with f(x)= f(y) which, using Tonio's point, immediately gives x= y.