Binary search obviously works on searching for elements in a sorted array. But if you think about the reason why it works is that the array itself is monotonic ( either increasing or decreasing ). So, if you are in a particular position, you can make a definite call whether the answer lies in the left part of the position or the right part of it.

A similar thing can be done with monotonic functions ( monotonically increasing or decreasing ) as well.

Let's say we have `f(x)`

which increases when x increases.

So, given a problem of finding x so that `f(x) = p`

, I can do a binary search for x.

In any instance,

1. if `f(current_position) > p`

, then I will search for values lower than current_position.

2. if `f(current_position) < p`

, then I will search for values higher than current_position

3. if `f(current_position) = p`

, then I have found my answer.

**Problems for practice**

SQRT