Let's say we have the following relationship between $f_1$ and $f_2$:
$$f_2(s) = \sqrt{1 + f_1(s)}$$
And $f_1$ returns a positive value. Why is it that minimax search using $f_2$ is guaranteed to the same action as using $f_1$ but is not guaranteed to return the same action as $f_1$ when used in expectimax search?
I understand that expectimax takes into account the weight of the arcs to compute the possible path. But I am still not able to understand how the aforementioned conclusion is being made.