Question: solving for a function y(x) that is the root of a function f(x,y)

I have a function of two variables, f(x,y).
The function does involve in infinite series of functions fn(x,y)

   f(x,y) = sum( fn(x,y) ,  n=-100..100)

but that shouldn't be an issue.

I need to solve numerically the roots of f, obtaining a stored function y(x) over a range x=0..1/2.

Finally, I take y(x) and evaluate another function, g[ x, y(x) ]  over the range of x.
g(x) would be plotted.

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