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Omni-MATH / Find all functions f:(0,∞)→(0,∞) such that

Problem

Answer published by the source. Consult the official source to check your work against its answer.

problem

Find all functions

f:(0,\infty) \to (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.

Plain-text mathematical notation (without MathML)

Find all functions f:(0,∞)→(0,∞) such that
f(x+(1)/(y))+f(y+(1)/(z))+f(z+(1)/(x))=1 for all x,y,z>0 with xyz=1.

Original LaTeX notation

Find all functions $f:(0,\infty) \to (0,\infty)$ 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 $xyz =1.$

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Source and history

task_id: 2572f509-74bd-51fe-a1b1-ca79075592ef
task_key: test--2572f509-74bd-51fe-a1b1-ca79075592ef
task_revision_id: 2
config / split: / test

Official source

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