An algebra problem by Brilliant Member

Algebra Level pending

Given a real function f(x) and a complex function z(xi), find the maximum number of roots the following functional equation can have: (f(x+2(f(x))) + z(xi))/(f(z(x(f(xi)))))

Hint: Let f(x) = 2i(f(zi))^2, z(0) = cf(x), where c is a constant and z(1) be undefined for all values of z.

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