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Question Number 214661 by efronzo1 last updated on 15/Dec/24

Answered by Rasheed.Sindhi last updated on 15/Dec/24

$$x.f\left(x\right)+x.f\left(\frac{1}{x}\right)=x+1$$$$f\left(x\right)+f\left(\frac{1}{x}\right)=\frac{x+1}{x}......A$$$$Replacexby\frac{1}{x}:$$$$f\left(\frac{1}{x}\right)+f\left(x\right)=\frac{\frac{1}{x}+1}{\frac{1}{x}}=x+1...B$$$$A\mathrm{\&}B:\frac{x+1}{x}=x+1$$$$x(x+1)-(x+1)=0$$$$(x+1)(x-1)=0$$$$x=\pm 1$$$$\mathcal{T}hegivenfunctionalequationis$$$$trueonlyforx=\pm 1$$

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