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Found problems: 1

2018 USAMO, 2
Tags: AMC , USA(J)MO , USAMO , function , 2018 USAMO Problem 2 , Hi
Find all functions $f:(0,\infty) \rightarrow (0,\infty)$ such that \[f\left(x+\frac{1}{y}\right)+f\left(y+\frac{1}{z}\right) + f\left(z+\frac{1}{x}\right) = 1\] for all $x,y,z >0$ with $xyz =1$.