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# Functions help

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Let be S the set of all nonzero real numbers. The function $$f : S \to \mathbb{R}$$ satisfies the following two properties:

(i) First,
$$f\left( \frac{1}{x} \right) = xf(x)$$ for all $$x \in S.$$

(ii) Second,
$$f \left( \frac{1}{x} \right) + f \left( \frac{1}{y} \right) = 1 + f \left( \frac{1}{x + y} \right)$$ for all $$x \in S$$ and $$y \in S$$ such that $$x + y \in S.$$

Let n be the number of possible values of $$f(1),$$ and let s be the sum of all possible values of $$f(1).$$ Find $$n \times s.$$

Apr 4, 2022

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ns = 10

Apr 5, 2022
#2
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Sorry, $$n\times s \neq 10.$$

SpaceXGeek  Apr 5, 2022
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Hello? I don't know how to bump this without doing this, sorry.

Apr 6, 2022