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OlympiadBench / 2171 / Find all functions f:Q→Q such that the equation

Problem

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

question

Find all functions

f: \mathbb{Q} \rightarrow \mathbb{Q}

such that the equation holds for all rational numbers

x

and

y

f(x f(x)+y)=f(y)+x^{2}

Here,

\mathbb{Q}

denotes the set of rational numbers.

Plain-text mathematical notation (without MathML)

Find all functions f:Q→Q such that the equation

holds for all rational numbers x and y.

f(xf(x)+y)=f(y)+x²

Here, Q denotes the set of rational numbers.

Original LaTeX notation

Find all functions $f: \mathbb{Q} \rightarrow \mathbb{Q}$ such that the equation

holds for all rational numbers $x$ and $y$.

$$
f(x f(x)+y)=f(y)+x^{2}
$$

Here, $\mathbb{Q}$ denotes the set of rational numbers.

answer type

Expression

is multiple answer

true

language

English

question type

Open-ended

subject

Math

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Source and history

upstream_id / Original problem ID: 2171
task_id: cd226db0-3f67-5d98-ba2f-5c4381f56bcc
task_key: OE~5fTO~5fmaths~5fen~5fCOMP--train--2171
task_revision_id: 3
config / split: OE_TO_maths_en_COMP / train

Official source

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