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OlympiadBench / 1718 / Denote by Q^(+)the set of all positive rational numbers. Determine…
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answer type
Expression
is multiple answer
false
language
English
question
Denote by the set of all positive rational numbers. Determine all functions which satisfy the following equation for all :
$$
f\left(f(x)^{2} y\right)=x^{3} f(x y)
\tag{1}
$$Plain-text mathematical notation (without MathML)
Denote by Q^(+)the set of all positive rational numbers. Determine all functions f:Q^(+)→Q^(+) which satisfy the following equation for all x,y∈Q^(+):
$$
f\left(f(x)^{2} y\right)=x^{3} f(x y)
\tag{1}
$$Original LaTeX notation
Denote by $\mathbb{Q}^{+}$the set of all positive rational numbers. Determine all functions $f: \mathbb{Q}^{+} \rightarrow \mathbb{Q}^{+}$ which satisfy the following equation for all $x, y \in \mathbb{Q}^{+}$:
$$
f\left(f(x)^{2} y\right)=x^{3} f(x y)
\tag{1}
$$question type
Open-ended
subject
Math
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