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Omni-MATH / Determine all functions f:R→R, where R is the set of all real numbers, satisfying the following two conditions: 1) There exists a real number M such that for every real number …

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problem

Determine all functions f:R→Rf:\mathbb{R}\to\mathbb{R}, where R\mathbb{R} is the set of all real numbers, satisfying the following two conditions: 1) There exists a real number MM such that for every real number x,f(x)<Mx,f(x)<M is satisfied. 2) For every pair of real numbers xx and yy, f(xf(y))+yf(x)=xf(y)+f(xy) f(xf(y))+yf(x)=xf(y)+f(xy) is satisfied.
Plain-text mathematical notation (without MathML)
Determine all functions f:R→R, where R is the set of all real numbers, satisfying the following two conditions:
1) There exists a real number M such that for every real number x,f(x)<M is satisfied.
2) For every pair of real numbers x and y,
f(xf(y))+yf(x)=xf(y)+f(xy)
is satisfied.
Original LaTeX notation
Determine all functions $f:\mathbb{R}\to\mathbb{R}$, where $\mathbb{R}$ is the set of all real numbers, satisfying the following two conditions:
1) There exists a real number $M$ such that for every real number $x,f(x)<M$ is satisfied.
2) For every pair of real numbers $x$ and $y$,
\[ f(xf(y))+yf(x)=xf(y)+f(xy)\]
is satisfied.

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Source and history

task_id
11fc3970-32e1-5ba2-a604-62b8964011a5
task_key
test--11fc3970-32e1-5ba2-a604-62b8964011a5
task_revision_id
1
config / split
/ test

Official source

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