Question

What is the function $f(x)$ which is differentiable everywhere and $f(x-1)f(x-2)+1=f(x)$?

score 461 · Answer 1 · 2020-09-23 23:05:20

What is the function $f(x)$ which is differentiable everywhere and $f(x-1)f(x-2)+1=f(x)$?

Published on 23 Sep 2020 - 23:05

score 223 · Answer 2 · 2020-09-24 11:40:39

Cauchy's Functional Equation $ f ( x + y ) = f ( x ) + f ( y ) $ with the Additional Assumption $ f \left( x ^ { n + 1 } \right) = x ^ n f ( x ) $

score 96 · Answer 3 · 2026-04-10 23:06:55

96

Views

A Strange but seemingly easy functional equation problem

Published on 10 Apr 2026 - 23:06

score 456 · Answer 4 · 2026-04-11 17:58:30

456

Views

Functional equation $f(x)f(f(x))=1$

Published on 11 Apr 2026 - 17:58

score 151 · Answer 5 · 2026-04-11 14:30:01

151

Views

Prove that identity function is a global minimum of a symmetric and quadratic functional

Published on 11 Apr 2026 - 14:30

score 342 · Answer 6 · 2020-09-27 05:41:44

342

Views

Prove that there is some constant $a\in \mathbb R$ such that $f(ax)=af(x)$ for every $x \in \mathbb R$

Published on 27 Sep 2020 - 5:41

score 159 · Answer 7 · 2026-04-12 03:59:57

159

Views

Two real functions with a given composition

Published on 12 Apr 2026 - 3:59

score 86 · Answer 8 · 2020-09-28 20:21:47

86

Views

Functions $f:\mathbb R\to\mathbb R$ satisfying $f\left(\frac{x+y}r\right)=\frac{f(x)+f(y)}s$

Published on 28 Sep 2020 - 20:21

score 599 · Answer 9 · 2020-09-28 21:55:57

599

Views

Which functions have the property $f(ab)=f(a)+f(b)$?

Published on 28 Sep 2020 - 21:55

score 65 · Answer 10 · 2026-04-12 15:56:40

65

Views

Elementary Symmetric Means as Quasi-Arithmetic Means

Published on 12 Apr 2026 - 15:56

score 59 · Answer 11 · 2020-09-29 20:20:53

59

Views

Find all solutions to the equation functional $f(x)+f(x+y)=y+2$

Published on 29 Sep 2020 - 20:20

score 84 · Answer 12 · 2026-04-08 21:18:57

84

Views

Functional equation involving composition and exponential

Published on 08 Apr 2026 - 21:18

score 118 · Answer 13 · 2020-09-30 20:29:20

118

Views

Solving the equation $\exp{y\left(x\right)} + y\left(x\right) + 1 = 0$ to find the function $y$

Published on 30 Sep 2020 - 20:29

score 34 · Answer 14 · 2026-04-12 15:46:58

34

Views

Understanding $z(a,b) \in[0,1]$ where $a=|x-y|$, $b=|y|$ and $x,y\in[-2,2]$

Published on 12 Apr 2026 - 15:46

score 58 · Answer 15 · 2020-10-03 06:20:09

58

Views

How to prove that a set of functions is equivalent to the other set of functions?

Published on 03 Oct 2020 - 6:20

List Question

What is the function $f(x)$ which is differentiable everywhere and $f(x-1)f(x-2)+1=f(x)$?

Cauchy's Functional Equation $ f ( x + y ) = f ( x ) + f ( y ) $ with the Additional Assumption $ f \left( x ^ { n + 1 } \right) = x ^ n f ( x ) $

A Strange but seemingly easy functional equation problem

Functional equation $f(x)f(f(x))=1$

Prove that identity function is a global minimum of a symmetric and quadratic functional

Prove that there is some constant $a\in \mathbb R$ such that $f(ax)=af(x)$ for every $x \in \mathbb R$

Two real functions with a given composition

Functions $f:\mathbb R\to\mathbb R$ satisfying $f\left(\frac{x+y}r\right)=\frac{f(x)+f(y)}s$

Which functions have the property $f(ab)=f(a)+f(b)$?

Elementary Symmetric Means as Quasi-Arithmetic Means

Find all solutions to the equation functional $f(x)+f(x+y)=y+2$

Functional equation involving composition and exponential

Solving the equation $\exp{y\left(x\right)} + y\left(x\right) + 1 = 0$ to find the function $y$

Understanding $z(a,b) \in[0,1]$ where $a=|x-y|$, $b=|y|$ and $x,y\in[-2,2]$

How to prove that a set of functions is equivalent to the other set of functions?

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