C is the correct answer. This is due to the fact that if we are adding functions then the x must be in the domain of both of the functions all the time. This is because when adding functions x must be present in both.
As for D it is possible to have x in the domain of g even if it is not in the domain of f/g since in this case it would be possible for g to equal zero but if f/g and g is zero then this would mean that you are dividing by zero and that would not be possible. But g by itself would include that x value.
A is not true since the product of the variables does not constitute that it will be the domain of fg, that is not how math works when combining functions.
B is also sometimes not true since X being in the domain of one function does not mean that it will be in the domain of g which would mean that f-g might not exist at x due to it being outside the domain
So in short if x is in the domain f+g, f-g then it is in the domain of both f and g. But if x is in f but not g means that x does not exist in f+g or f-g. Im sorry if this is confusing msg me if you need more help.
May 26th, 2015
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