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Mathematics, 29.07.2021 18:50 ozheng24112

Let f(x) = \frac{1}{x} and g(x)= \left \{ {{\frac{1}{x}} if x\  \textgreater \ 0 \atop {2+\frac{1}{x} }} if x\  \textless \ 0 \right.

Show that f'(x) = g'(x) for all x domains. Can we conclude from the corollary below that f-g is constant?

[If f'(x) = g'(x) for all x in an interval (a, b) then f - g is constant on (a, b); that is, f(x) = g(x) + c where c is a constant.

fins f'(x) and g'(x)

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