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Question Number 164039 by ArielVyny last updated on 13/Jan/22

$$considerffunctionDf=[0,1]$$$$f\left(0\right)=f\left(1\right)c\in [0,\frac{1}{2}]showthatf\left(c\right)=f(c+\frac{1}{2})$$

Answered by Ar Brandon last updated on 13/Jan/22

$$f\left(0\right)=f\left(1\right)$$$$f(c+0)=f(c+1),\mathrm{since}f<1-\mathrm{periodic}$$$$f\left(c\right)=f((c+\frac{1}{2})+\frac{1}{2})=f(c+\frac{1}{2})$$$$\mathrm{Hence}f\left(c\right)=f(c+\frac{1}{2})$$

Commented by Ar Brandon last updated on 13/Jan/22

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