Produce decision version of the problem

Question

An optimisation problem requires minimising some function $f(x)$, where $x$ is a vector of integers. What is the corresponding decision version of the problem?

Answer 1

"Given $f(x)$, what is $\min(f(x))$?" becomes "Given $f(x)$, and $k$, decide if there is an $x$ such that $f(x)< k$?"