If $g \in I$ for an ideal $I$ over a commutative ring $R$, and $f \not \in I$, what can we say about $f-g$?

Question

This is a really basic question:

Let $R$ be a commutative ring and $I \trianglelefteq R$ be an ideal.

Let $g \in I$ and let $f \not \in I$.

Can we say for certain that $f - g \not \in I$?

A classmate points out that you could say that

$$g+I =I$$ so that $$(f+(-g))+I = f+I \neq I.$$