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Question Number 218256 by mr W last updated on 03/Apr/25

Answered by efronzo1 last updated on 03/Apr/25

$$\mathrm{f}\left(3\right)+\mathrm{f}(-\frac{1}{2})=72$$$$\mathrm{f}(-\frac{1}{2})+\mathrm{f}\left(\frac{2}{3}\right)=-12$$$$\mathrm{f}\left(\frac{2}{3}\right)+\mathrm{f}\left(3\right)=16$$$$2\{\mathrm{f}\left(3\right)+\mathrm{f}(-\frac{1}{2})+\mathrm{f}\left(\frac{2}{3}\right)\}=76$$$$\mathrm{f}\left(3\right)+(-12)=38$$$$\mathrm{f}\left(3\right)=50$$

Commented by mr W last updated on 04/Apr/25

$$thanks!$$

Answered by mahdipoor last updated on 03/Apr/25

$$f\left(x\right)+f\left(\frac{1}{1-x}\right)=24x$$$$f\left(\frac{1}{1-x}\right)+f\left(\frac{1-x}{-x}\right)=\frac{24}{1-x}$$$$f\left(\frac{1-x}{-x}\right)+f\left(x\right)=\frac{24(1-x)}{-x}$$$$\Rightarrow \Rightarrow f\left(x\right)=12(x+\frac{1}{1-x}-\frac{1-x}{x})$$

Commented by mr W last updated on 04/Apr/25

$$thanks!$$

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