Question Number 171146 by akolade last updated on 08/Jun/22
Commented by cortano1 last updated on 08/Jun/22
$$\:\mathrm{5}{f}\left(\frac{\mathrm{1}}{{x}}\right)={f}\left({x}\right)+\sqrt{{x}}\:...\left(\mathrm{1}\right) \\ $$$$\:\:{f}\left(\frac{\mathrm{1}}{{x}}\right)=\mathrm{5}{f}\left({x}\right)−\frac{\mathrm{1}}{\:\sqrt{{x}}}\:...\left(\mathrm{2}\right) \\ $$$$\left(\mathrm{1}\right)−\mathrm{5}\left(\mathrm{2}\right) \\ $$$$\Rightarrow\mathrm{0}=−\mathrm{24}{f}\left({x}\right)+\sqrt{{x}}+\frac{\mathrm{5}}{\:\sqrt{{x}}} \\ $$$$\Rightarrow{f}\left({x}\right)=\frac{\sqrt{{x}}}{\mathrm{24}}\:+\frac{\mathrm{5}}{\mathrm{24}\sqrt{{x}}}\: \\ $$
Commented by SLVR last updated on 10/Jun/22
$${nice} \\ $$