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Question Number 154542 by SANOGO last updated on 19/Sep/21

Answered by qaz last updated on 19/Sep/21

$$\mathrm{Let}\mathrm{f}\left(\mathrm{x}\right)=\mathrm{ax}+\mathrm{b}$$$${\mathrm{ax}}^2+\mathrm{bx}={\mathrm{x}}^2+\mathrm{a}{\int }_0^{\mathrm{x}}(\mathrm{x}-\mathrm{t})\mathrm{dt}={\mathrm{x}}^2+\mathrm{a}{(\mathrm{xt}-\frac{1}{2}{\mathrm{t}}^2)}_0^{\mathrm{x}}={\mathrm{x}}^2+\frac{1}{2}{\mathrm{ax}}^2$$$$\Rightarrow \mathrm{a}=2\mathrm{b}=0$$$$\Rightarrow \mathrm{f}\left(1\right)=2$$

Commented by SANOGO last updated on 19/Sep/21

$$mercibien$$

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