New type of series!

Number Theory Level 5

Given that $\sum_{p=prime}\dfrac{(f+g)(p)}{p^s}=\sum_{p=prime}\dfrac{(f*g)(p)}{p^s}$ where $f* g$ is a dirichlet convolution then this is always true (assuming both sides converges) if f,g are

multiplicative,additive multiplicative,multiplicative, No restriction required, always true. additive,additive