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Question Number 174570 by blackmamba last updated on 04/Aug/22

$$\{\begin{array}{l}\mathit{f}\left(\frac{\mathit{x}}{{\mathit{x}}^2+1}\right)=\frac{{\mathit{x}}^2}{{\mathit{x}}^4+2{\mathit{x}}^2+1}\\ \mathit{f}\left(\sqrt{3}\right)=?\end{array}$$

Commented by infinityaction last updated on 04/Aug/22

$$f\left(\frac{1}{x+\frac{1}{x}}\right)=\frac{1}{{(x+\frac{1}{x})}^2}$$$$f\left(\sqrt{3}\right)=3$$

Answered by Rasheed.Sindhi last updated on 05/Aug/22

$$f\left(\frac{x}{x^2+1}\right)=\frac{x^2}{x^4+2x^2+1}$$$$f\left(\frac{x}{x^2+1}\right)={\left(\frac{x}{x^2+1}\right)}^2$$$$Replacing\frac{x}{x^2+1}byx$$$$\overline{)\begin{array}{c}f\left(x\right)=x^2\end{array}}$$$$f\left(\sqrt{3}\right)={\left(\sqrt{3}\right)}^2=3$$

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