Question 1
Find all functions $f:\mathbb Q_{>0}\to\mathbb Q_{>0}$ such that, for every $x,y\in\mathbb Q_{>0}$,
$$\frac{f(x)f(y)}{f(xy)}=\frac{(\sqrt{f(x)}+\sqrt{f(y)})^2}{f(x+y)}.$$
Question point values reproduce the supplied source labels; no automatic proof grading is implied.
$$\frac{f(x)f(y)}{f(xy)}=\frac{(\sqrt{f(x)}+\sqrt{f(y)})^2}{f(x+y)}.$$
Question point values reproduce the supplied source labels; no automatic proof grading is implied.