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Question Number 153898 by mathdanisur last updated on 11/Sep/21

$$\mathrm{Find}\mathrm{all}\mathrm{functions}\mathrm{f}:\mathrm{Q}\to \mathrm{Q}\mathrm{satisfying}$$$$\mathrm{these}\mathrm{followong}\mathrm{conditions}\mathrm{for}\mathrm{all}\mathbf{x}\in \mathrm{Q}$$$$1.\mathrm{f}(\mathrm{x}+1)=\mathrm{f}\left(\mathrm{x}\right)+1$$$$2.\mathrm{f}\left({\mathrm{x}}^3\right)={\mathrm{f}}^3\left(\mathrm{x}\right)$$

Answered by talminator2856791 last updated on 12/Sep/21

$$$$$$1.f(x+1)=f\left(x\right)+1$$$$f\left(x\right)=x+k,k\in \mathbb{R}$$$$$$$$2.f\left(x^3\right)={\left(f\left(x\right)\right)}^3$$$$f\left(x\right)=x^k,k\in \mathbb{R}$$$$$$

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