Ecuatie functionala

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Mateescu Constantin
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Ecuatie functionala

Post by Mateescu Constantin »

Fie \( f: (0,\infty) \rightarrow (0,\infty ) \) o functie neconstanta, care pentru orice \( x,y,z\in (0,\infty) \) satisface relatia:

\( f(x)f(yf(x))f(zf(x+y))=f(x+y+z) \).

Sa se arate ca \( f \) este injectiva si sa se determine toate aceste functii.
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