Can I Avoid Eval() Here?

I am trying to assign an "onclick" event to a dynamically-created DOM
element (an image).

I have read countless times that "eval()" is to be avoided at all costs.
However, I cannot seem to get my new onclick to work without it.

Here's what I have so far:

myeval = 'detachFile(this);'
detachImage = getElementById('detach-jfhahhf');
detachImage.onclick = function() { eval(myeval) }

This works perfectly fine for me, but this is a web-app that will be
exposed to public users, and I obviously don't want them being able to
eval anything if i can help it.

Can that be done without the eval()?