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By far the most common mistake is carelessness in distributing the minus through the terms of g, resulting in some term having the wrong sign. Fortunately, this is an easy one to find and fix by picking 1 or 2 easy values of x and spot checking f(x), g(x), and (f-g)(x) at those specific points. A more subtle technicality is caused by domain mismatches. Recall that (f-g)(4) is only defined when both f(4) and g(4) are defined, even if (f-g)(x) looks algebraically like it should be defined as x=4.

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