Question

can you divide a function by e^x?

Answer 1

Hmm weird question :)

So like if we divided a function by x,\[\Large \frac{f(x)}{x}, \qquad\qquad x\ne0\]We can do it, yes, but we lose the point x=0.
Is this maybe what your question is about?
When we divide a function by e^x do we lose any points?\[\Large \frac{f(x)}{e^x}\]