Example of $f(x)-f(y)=g(x-y)$

101 Views Asked by At

we know that for linear function $f(x)-f(y)=f(x-y)$ for all $x, y\in D$.

Now, I am wondering, if we replace the $f$ in the right hand side of the equality by some nonlinear $g$, are there any other nonlinear example $f$ such that

for any $x$ and $y$ in the domain, there exists a function $g$:

$f(x)-f(y)=g(x-y)$ for all $x, y\in D$ for some $g$

Thank you