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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.

question

Find all functions f:R→Rf: \mathbb{R} \rightarrow \mathbb{R} that satisfy the conditions f(1+xy)−f(x+y)=f(x)f(y) for all x,y∈R f(1+x y)-f(x+y)=f(x) f(y) \text { for all } x, y \in \mathbb{R} and f(−1)≠0f(-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 $f(-1) \neq 0$.

answer type

Expression

is multiple answer

false

language

English

question type

Open-ended

subject

Math

Discussion

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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
4
config / split
OE_TO_maths_en_COMP / train

Official source

initial import