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Math  /  Algebra

QuestionTrouver toutes les applications ff définies de R∗\boldsymbol{R}^{*} dans R′R^{\prime} telles que: (∀x∈R)f(1x)=x+1+x2(\forall x \in R) f\left(\frac{1}{x}\right)=x+\sqrt{1+x^{2}}

Studdy Solution
On a trouvé deux expressions pour f(x)f(x) !
Si x>0x > 0, f(x)=1+1+x2xf(x) = \frac{1 + \sqrt{1 + x^2}}{x}.
Si x<0x < 0, f(x)=1−1+x2xf(x) = \frac{1 - \sqrt{1 + x^2}}{x}.

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