# complexity theory – Hardness of a problem which is the sum of two NP-Hard problems

Consider the problem of computing an exponential sum over a certain function $$g(x)=f(x)+h(x)$$, that is computing

$$sum_{x}g(x)=sum_{x}f(x)+sum_{x}h(x)$$

now if we know that $$sum_{x}f(x)$$ and $$sum_{x}h(x)$$ are two NP-Hard problems, what can we say about the hardness of $$sum_{x}g(x)$$?