Let f(x) = 1/x and Show that f'(x) = g'(x) for all x in their domain. Can

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Let f(x) = 1/x and
If x>0 g(x) = 1+ - If x< 0

Show that f'(x) = g'(x) for all x in their domain. Can we conclude from Corollary 7 that f - g is constant?

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