Ambiguity in Odd and Even Function Question

GRE Quant Problem Solving
1

If f(x) and g(x) are even functions, f(x) + g(x) is an even function.

True
False

Select one answer choice.

The answer given is true, but if consider a case where, f(x) = x^2
g(x) = -x^2, Both of the are even but f(x) + g(x) = 0

and y = 0 is both an even and odd function (apply the formal definition to it) , hence it is not always even, it can be odd as well or ambiguous in nature

Thoughts

2

So, f(x) + g(x) = 0 is an even function which proves the statement “If f(x) and g(x) are even functions, f(x) + g(x) is an even function.” f(x) + g(x) might also be odd function like in your example but that doesn’t change the fact f(x) + g(x) will always be an even function

3

Thank you so much

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