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OlympiadBench / 1659 / Find all functions f:R^(+)→R^(+) such that

Problem

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

question

Find all functions

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

such that

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

for all

x, y \in \mathbb{R}^{+}

. (Symbol

\mathbb{R}^{+}

denotes the set of all positive real numbers.)

Plain-text mathematical notation (without MathML)

Find all functions f:R^(+)→R^(+) such that

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

for all x,y∈R^(+). (Symbol R^(+)denotes the set of all positive real numbers.)

Original LaTeX notation

Find all functions $f: \mathbb{R}^{+} \rightarrow \mathbb{R}^{+}$ such that

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

for all $x, y \in \mathbb{R}^{+}$. (Symbol $\mathbb{R}^{+}$denotes the set of all positive real numbers.)

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: 1659
task_id: c2f02a77-39b0-512e-81b9-f84bc6a9a0be
task_key: OE~5fTO~5fmaths~5fen~5fCOMP--train--1659
task_revision_id: 3
config / split: OE_TO_maths_en_COMP / train

Official source

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