# Complexity of approximating a function value using queries

I am looking for information on problems of the following kind.

There is a function $$f: [0,1] \to \mathbb{R}$$ that is continuous and monotonically-increasing, with $$f(0)<0$$ and $$f(1)>0$$. You have to find the unique $$x\in[0,1]$$ such that $$f(x)=0$$. You can access $$f$$ only through queries of the type "what is $$f(x)$$?". How many such queries do you need in order to approximate $$x$$ up to some constant $$\epsilon$$?

Here, the solution is simple: using binary search, the interval in which $$x$$ can lie shrinks by 2 after each query, so $$\log_2(1/\epsilon)$$ queries are sufficient. This is also an upper bound, since an adversary can always answer in such a way that the possible interval for $$x$$ shrinks by at most 2 after each query.

However, one can think of more complicated problems of this kind, with several different functions and possibly different kinds of queries.

What is a term, and some references, for this kind of computational problems?