How do I compute zeros of a function numerically?

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Say I have a function h(x), so that:

g(x) < h(x) < f(x) or f(x) < h(x) < g(x)

How can I find the zeros of h(x) without knowing h(x)? I mean, numerically.

I know h(x) has 3 zeros. But I only know the intervals due to f(x) and g(x) . Is the median of this intervals the best approximation to h(x)=0 ?

By the way, I'm using Wolfram Mathematica.

functions f(x) and g(x)

graph of the functions, with the area where h(x) may be