Question Number 138316 by Ñï= last updated on 12/Apr/21
$${f}\left({x}\right)=\frac{\mathrm{1}}{\:\sqrt{\mathrm{1}+{x}}}+\frac{\mathrm{1}}{\:\sqrt{\mathrm{1}+{a}}}+\sqrt{\frac{{ax}}{{ax}+\mathrm{8}}}\:\:\:\:\:\:\:\:,{x}\in\left(\mathrm{0},\infty\right) \\ $$$$\forall\:{a}\in\left(\mathrm{0},\infty\right),{show}\:\mathrm{1}<{f}\left({x}\right)<\mathrm{2}. \\ $$