Can an even function ever be injective?

Question

In the first few lessons of an introductory Calculus class, there is this exercise:

We say that a function $f$: $R → R$ is even if $f(−x) = f(x)$. Can an even function ever be injective?

My proof is as follows and I am wondering if it is correct:

let $y=-x$
$f(y)=f(x)$
$y\neq x$
$\therefore$ No, an even function can never be injective

As long as you choose $y = -x \neq 0$, you're all good – Mike Daas Aug 02 '22 at 21:56 — Mike Daas, Aug 02 '22 at 21:56

score 4 · Accepted Answer · answered Aug 02 '22 at 21:58

4

This is perfectly fine. Since $f(1) = f(-1)$ does not imply $1=-1$, as an example, the function is not injective.

answered Aug 02 '22 at 21:58

PrincessEev

1 Answers1