Let R be ring, I ideal of R

Let f is automorphism of R.

let say: (f(x)+4 )f(y)=0, $\displaystyle \forall$ x,y $\displaystyle \in $ I

if i say $\displaystyle {f}^{-1 }$ (f(x)+4 ) y = 0, $\displaystyle \forall$ x,y $\displaystyle \in $

whether the statement was valid?

if yes, any reason to explain that? (i know f is invertible cause f is 1-1, but whether there is a more specific explanation?)