Prove or Disprove if the Function is Injective

Prove or Disprove if the Function is Injective
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[@platosbeard3476]

Let f:R-->R be an arbitrary even function. From the definition of an even function, f(x)=f(-x). So, let x!=0, a=x and b=-x, hence, f(a)=f(b) and a!=b, which proves no even function from R to R is injective. I think this is OK? Taking an "arbitrary function" would mean it isn't first order logic, though, and I've not done anything with HOL so I'm not sure

[@datepicboi4870]

Thank you from Palestine😃

[@STUDY-x1y]

Ok but how do you prove it then? Do we have to then show the infinite number of times it doesn't fail?

[@etheroxxx]

Thank you from Australia !

[@DaiMoscv]

Thank you from Italy :)

[@holtzmanoren99]

Thank you from Israel😃

[@TheMathSorcerer]

Wow Israel very cool!! Thank you 😃😃😃😃