A function problem ("compute $f(x)$") can easily be converted into a decision problem of deciding its graph ("is $f(x) = y$ true?"). However, this may change the computational complexity of the problem (https://en.wikipedia.org/wiki/Decision_problem#Function_problems). For example, computing Ackermann function is not PR, but its graph is (https://mathoverflow.net/questions/76037/inverse-ackermann-primitive-recursive-or-not).
Then, can we convert any function problem into an equally difficult decision problem? For example, can we make a decision problem that require computing Ackermann function to solve?
I think some good cryptographic hash function $h()$ may be useful (we can make a problem "is $h(f(x)) = y$ true?" and it will require computation of $f(x)$), but I'm not familiar with hash functions and could not prove it.
I will appreciate any help. Thank you for your attention.