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OlympiadBench / 1879 / Let R^(+)be the set of positive real numbers. Determine all functions…

Problem

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

question

Let

\mathbb{R}^{+}

be the set of positive real numbers. Determine all functions

f: \mathbb{R}^{+} \rightarrow \mathbb{R}^{+}

such that, for all positive real numbers

x

and

y

$$
f(x+f(x y))+y=f(x) f(y)+1
\tag{*}
$$

Plain-text mathematical notation (without MathML)

Let R^(+)be the set of positive real numbers. Determine all functions f:R^(+)→R^(+) such that, for all positive real numbers x and y,

$$
f(x+f(x y))+y=f(x) f(y)+1
\tag{*}
$$

Original LaTeX notation

Let $\mathbb{R}^{+}$be the set of positive real numbers. Determine all functions $f: \mathbb{R}^{+} \rightarrow \mathbb{R}^{+}$ such that, for all positive real numbers $x$ and $y$,

$$
f(x+f(x y))+y=f(x) f(y)+1
\tag{*}
$$

answer type

Expression

is multiple answer

false

language

English

question type

Open-ended

subject

Math

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Source and history

upstream_id / Original problem ID: 1879
task_id: d64c6a64-7a81-55a6-83cd-f1f363d1fa79
task_key: OE~5fTO~5fmaths~5fen~5fCOMP--train--1879
task_revision_id: 3
config / split: OE_TO_maths_en_COMP / train

Official source

initial import