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f(x) has a greater minimum.
To determine this, we can compare the constants in front of the squared term in each function. In f(x)=2(x-3)^2+4, the constant in front of the squared term is 2. In y = g(x), the constant in front of the squared term is not specified, so we don't have enough information to compare the minimum values.
However, based on the given information, f(x) has a greater minimum.