Difference between revisions of "2022 OIM Problems/Problem 3"

Revision as of 02:38, 14 December 2023

Let $\mathbb{R}$ be the set of real numbers. Find all functions $f : \mathbb{R} \to \mathbb{R}$ satisfying the following conditions simultaneously:

(i) $f(yf(x)) + f(x − 1) = f(x)f(y)$ (Error compiling LaTeX. Unknown error_msg) for every $x, y$ in $\mathbb{R}$ .

(ii) $|f(x)| < 2022$ for every $x$ with $0 < x < 1$ .

This problem needs a solution. If you have a solution for it, please help us out by adding it.

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 == Problem ==
-Let <math>\mathbb{R}</math> be the set of real numbers. Find all functions <math>f : \mathbb{R} \to \mathbb{R} satisfying the following conditions simultaneously:
+Let <math>\mathbb{R}</math> be the set of real numbers. Find all functions <math>f : \mathbb{R} \to \mathbb{R}</math> satisfying the following conditions simultaneously:
-(i) </math>f(yf(x)) + f(x − 1) = f(x)f(y)<math> for every </math>x, y<math> in </math>\mathbb{R}<math>.
+(i) <math>f(yf(x)) + f(x − 1) = f(x)f(y)</math> for every <math>x, y</math> in <math>\mathbb{R}</math>.
-(ii) </math>|f(x)| < 2022<math> for every </math>x<math> with </math>0 < x < 1$.
+(ii) <math>|f(x)| < 2022</math> for every <math>x</math> with <math>0 < x < 1</math>.
 == Solution ==