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OlympiadBench / 2147 / Find all functions f:R→R that satisfy the…

Problem

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

answer type

Expression

is multiple answer

false

language

English

question

Find all functions

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

that satisfy the conditions

f(1+x y)-f(x+y)=f(x) f(y) \text { for all } x, y \in \mathbb{R}

and

f(-1) \neq 0

Plain-text mathematical notation (without MathML)

Find all functions f:R→R that satisfy the conditions

f(1+xy)−f(x+y)=f(x)f(y) for all x,y∈R

and f(−1)≠0.

Original LaTeX notation

Find all functions $f: \mathbb{R} \rightarrow \mathbb{R}$ that satisfy the conditions

$$
f(1+x y)-f(x+y)=f(x) f(y) \text { for all } x, y \in \mathbb{R}
$$

and $f(-1) \neq 0$.

question type

Open-ended

subject

Math

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Source and history

upstream_id / Original problem ID: 2147
task_id: 5951ee2e-526c-5b63-b400-c3f14cd94b2e
task_key: OE~5fTO~5fmaths~5fen~5fCOMP--train--2147
task_revision_id: 1
config / split: OE_TO_maths_en_COMP / train

Official source

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