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Omni-MATH / Find all functions f: (0, infty) mapsto (0, infty) (so f is a function from the positive real numbers) such that …

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problem

Find all functions $ f: (0, \infty) \mapsto (0, \infty)$ (so f f is a function from the positive real numbers) such that \[ \frac {\left( f(w) \right)^2 \plus{} \left( f(x) \right)^2}{f(y^2) \plus{} f(z^2) } \equal{} \frac {w^2 \plus{} x^2}{y^2 \plus{} z^2} \] for all positive real numbers w,x,y,z, w,x,y,z, satisfying $ wx \equal{} yz.$ [i]Author: Hojoo Lee, South Korea[/i]
Plain-text mathematical notation (without MathML)
Find all functions $ f: (0, \infty) \mapsto (0, \infty)$ (so f is a function from the positive real numbers) such that
\[ \frac {\left( f(w) \right)^2 \plus{} \left( f(x) \right)^2}{f(y^2) \plus{} f(z^2) } \equal{} \frac {w^2 \plus{} x^2}{y^2 \plus{} z^2}
\]
for all positive real numbers w,x,y,z, satisfying $ wx \equal{} yz.$


[i]Author: Hojoo Lee, South Korea[/i]
Original LaTeX notation
Find all functions $ f: (0, \infty) \mapsto (0, \infty)$ (so $ f$ is a function from the positive real numbers) such that
\[ \frac {\left( f(w) \right)^2 \plus{} \left( f(x) \right)^2}{f(y^2) \plus{} f(z^2) } \equal{} \frac {w^2 \plus{} x^2}{y^2 \plus{} z^2}
\]
for all positive real numbers $ w,x,y,z,$ satisfying $ wx \equal{} yz.$


[i]Author: Hojoo Lee, South Korea[/i]

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Source and history

task_id
f4d7b7e4-f61d-5867-affb-93bbccca5660
task_key
test--f4d7b7e4-f61d-5867-affb-93bbccca5660
task_revision_id
1
config / split
/ test

Official source

initial import