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Question Number 119801 by Ar Brandon last updated on 27/Oct/20

$$\mathrm{If}f:\mathbb{R}\to \mathbb{R}\mathrm{is}\mathrm{a}\mathrm{function}\mathrm{such}\mathrm{that}f\left(0\right)=1\mathrm{and}f(\mathrm{x}+f\left(\mathrm{y}\right))=$$$$f\left(\mathrm{x}\right)+\mathrm{y}\mathrm{for}\mathrm{all}\mathrm{x},\mathrm{y}\in \mathbb{R},\mathrm{then}$$$$\left(\mathrm{A}\right)1\mathrm{is}\mathrm{a}\mathrm{period}\mathrm{of}f$$$$\left(\mathrm{B}\right)f\left(n\right)=1\mathrm{for}\mathrm{all}\mathrm{integers}n$$$$\left(\mathrm{C}\right)f\left(n\right)=n\mathrm{for}\mathrm{all}\mathrm{integers}n$$$$\left(\mathrm{D}\right)f(-1)=0$$

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