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Question Number 54504 by afachri last updated on 05/Feb/19

$$\mathbf{please},\mathbf{Sir}.\mathbf{Would}\mathbf{u}\mathbf{explain}\mathbf{to}\mathbf{me}\mathbf{how}?$$$$\mathbf{if}\mathit{f}\left(\frac{\mathit{x}}{\mathit{x}-1}\right)+2\mathit{f}\left(\frac{\mathit{x}-1}{\mathit{x}}\right)=\frac{\mathit{x}}{\mathit{x}-1},$$$$\mathbf{then}\mathit{f}\left(\mathit{x}\right)\mathbf{is}....$$

Answered by tanmay.chaudhury50@gmail.com last updated on 05/Feb/19

$$f\left(a\right)+2f\left(\frac{1}{a}\right)=a\times 2$$$$f\left(\frac{1}{a}\right)+2f\left(a\right)=\frac{1}{a}\times 1$$$$$$$$2f\left(a\right)+4f\left(\frac{1}{a}\right)=2a$$$$2f\left(a\right)+f\left(\frac{1}{a}\right)=\frac{1}{a}$$$$so3f\left(\frac{1}{a}\right)=2a-\frac{1}{a}$$$$3f\left(\frac{1}{a}\right)=(\frac{2}{\frac{1}{a}}-\frac{1}{a})$$$$f\left(\frac{1}{a}\right)=\frac{1}{3}(\frac{2}{\frac{1}{a}}-\frac{1}{a})$$$$f\left(x\right)=\frac{1}{3}(\frac{2}{x}-x)$$

Commented by afachri last updated on 05/Feb/19

$$ahaaa.iwascuriousandgettingstuck$$$$howtosolveit.instead{it}^{\prime }ssimple.$$$$ThankYousomuchMrTanmay.$$

Commented by tanmay.chaudhury50@gmail.com last updated on 05/Feb/19

$$mostwelcomesir...$$

Commented by Joel578 last updated on 06/Feb/19

$$\mathrm{Mr}.\mathrm{Afachri},\mathrm{are}\mathrm{u}\mathrm{from}\mathrm{Indonesia}?$$

Commented by afachri last updated on 08/Feb/19

$$\mathrm{yes}\mathrm{i}\mathrm{am}\mathbf{M}r\mathbf{Joel}.\mathbf{A}reyou??$$

Commented by Joel578 last updated on 08/Feb/19

$$\mathrm{wah}\mathrm{sama},\mathrm{hehehe}$$

Commented by afachri last updated on 08/Feb/19

$$aseekkketemusamasamadisini.$$$$mohonbimbingannya.Mainbrainly$$$$juga??$$$$$$

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