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x-x-r-where-x-0-and-0-lt-r-1-shown-that-for-any-x-y-R-2-x-y-x-y-please-




Question Number 120272 by cantor last updated on 30/Oct/20
ϕ(x)=x^r   where x∈[0,+∞[ and 0<r≤1  shown that for any (x,y)∈R_+ ^2   𝛟(x+y)≤𝛟(x)+𝛟(y)      please
$$\varphi\left({x}\right)=\boldsymbol{{x}}^{\boldsymbol{{r}}} \\ $$$$\boldsymbol{{where}}\:\boldsymbol{{x}}\in\left[\mathrm{0},+\infty\left[\:\boldsymbol{{and}}\:\mathrm{0}<\boldsymbol{{r}}\leqslant\mathrm{1}\right.\right. \\ $$$${shown}\:{that}\:{for}\:{any}\:\left(\boldsymbol{{x}},\boldsymbol{{y}}\right)\in\mathbb{R}_{+} ^{\mathrm{2}} \\ $$$$\boldsymbol{\varphi}\left(\boldsymbol{{x}}+\boldsymbol{{y}}\right)\leqslant\boldsymbol{\varphi}\left(\boldsymbol{{x}}\right)+\boldsymbol{\varphi}\left(\boldsymbol{{y}}\right) \\ $$$$\:\:\:\:\boldsymbol{{please}} \\ $$

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