Question Number 108815 by 1xx last updated on 19/Aug/20
$${f}\left({x}\right)=\frac{\mathrm{1}}{\:\sqrt{\mathrm{1}+{x}}}+\frac{\mathrm{1}}{\:\sqrt{\mathrm{1}+{a}}}+\frac{\sqrt{{ax}}}{\:\sqrt{{ax}+\mathrm{8}}} \\ $$$${x}>\mathrm{0}\:,\:{a}>\mathrm{0}\:,\:{x}\in{R},\:{a}\in{R} \\ $$$${prove}:\mathrm{1}<{f}\left({x}\right)<\mathrm{2} \\ $$