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Question Number 165774 by mathlove last updated on 08/Feb/22

Answered by Eulerian last updated on 08/Feb/22

$$\mathrm{let}:\frac{1}{\mathrm{x}-3}=\mathrm{y}$$$$\mathrm{x}=\frac{1}{\mathrm{y}}+3\Rightarrow \mathrm{y}=\frac{1}{\mathrm{x}}+3$$$$$$$$\therefore$$$$\mathrm{f}\left(\frac{1}{\frac{1}{\mathrm{x}}+3-3}\right)=\frac{1}{(\frac{1}{\mathrm{x}}+3)}$$$$\mathrm{f}\left(\mathrm{x}\right)=\frac{1}{(\frac{1}{\mathrm{x}}+3)}$$

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