Question

Let $f(x)$ be a fourth differentiable function such that $f(2x^2-1)=2xf(x)$, $\forall x \in \mathbb R$, then $f^{(4)}(0)$ is equal to?

score 560 · Answer 1 · 2026-04-15 08:00:13

560

Views

Let $f(x)$ be a fourth differentiable function such that $f(2x^2-1)=2xf(x)$, $\forall x \in \mathbb R$, then $f^{(4)}(0)$ is equal to?

Published on 15 Apr 2026 - 8:00

score 146 · Answer 2 · 2026-04-18 07:50:36

146

Views

Real functions with the property: $\ f(x_1)f(x_2) = f\left( \frac{x_1+x_2}{2} \right)^2 $ for all $\ x_1,\ x_2\in\mathbb{R}.\ $

Published on 18 Apr 2026 - 7:50

score 102 · Answer 3 · 2026-04-20 01:59:38

102

Views

$(x-y)(f(f(x)^2)-f(f(y)^2))=(f(x)-f(y))(f(x)^2-f(y)^2$

Published on 20 Apr 2026 - 1:59

score 59 · Answer 4 · 2026-04-09 02:20:37

59

Views

Functional equation for cosine on $[0,\frac{\pi}{2}]$

Published on 09 Apr 2026 - 2:20

score 61 · Answer 5 · 2026-04-11 04:14:52

61

Views

Does this functional equation have a solution (also is there free functional equation solving software)?

Published on 11 Apr 2026 - 4:14

score 174 · Answer 6 · 2026-04-17 13:54:09

174

Views

Find $f$ such that $xf(x)+x^2f(x-1)=f(x^2)$

Published on 17 Apr 2026 - 13:54

score 175 · Answer 7 · 2026-04-14 04:20:59

175

Views

A functional equation problem: $f(f(x))=x^2-x+1$

Published on 14 Apr 2026 - 4:20

score 176 · Answer 8 · 2026-04-17 12:04:07

Find all functions $f:\mathbb{N}\rightarrow\mathbb{N}$ such that $\gcd(f(m),n) + \text{lcm}(m,f(n)) = \text{lcm}(f(m),n) + \gcd(m,f(n))$

score 21 · Answer 9 · 2026-04-09 07:06:43

21

Views

Solve a parametered function equation

Published on 09 Apr 2026 - 7:06

score 162 · Answer 10 · 2026-04-14 16:40:26

162

Views

How many functions respect the equation $3f(f(x))-7f(x)+2x=0$

Published on 14 Apr 2026 - 16:40

score 55 · Answer 11 · 2026-04-15 16:59:25

55

Views

Does there exist a non-constant solution to this (and other similar) functional equations?

Published on 15 Apr 2026 - 16:59

score 69 · Answer 12 · 2026-04-16 08:56:15

69

Views

Why doesn't solving this functional equation in this way work?

Published on 16 Apr 2026 - 8:56

score 398 · Answer 13 · 2026-04-16 20:58:36

398

Views

Find all functions $f:\mathbb R \rightarrow \mathbb R$ such that $x^2\cdot f(x)+f(1-x)=2x-x^4$ $\forall\; x\in \mathbb R$

Published on 16 Apr 2026 - 20:58

score 76 · Answer 14 · 2026-04-14 22:28:02

76

Views

If $d(x, y) = |f(x) - f(y)|$ is invariant under reflections of the real line, can we deduce $d(x, y) = \alpha |x-y|$?

Published on 14 Apr 2026 - 22:28

score 118 · Answer 15 · 2026-04-17 12:04:08

118

Views

Find all functions $f: \mathbb R \rightarrow \mathbb R$ such that $f(xf(x)+f(y))=(f(x))^2+y$ $\; \forall \; x,y \; \in \mathbb R$

Published on 17 Apr 2026 - 12:04

List Question

Let $f(x)$ be a fourth differentiable function such that $f(2x^2-1)=2xf(x)$, $\forall x \in \mathbb R$, then $f^{(4)}(0)$ is equal to?

Real functions with the property: $\ f(x_1)f(x_2) = f\left( \frac{x_1+x_2}{2} \right)^2 $ for all $\ x_1,\ x_2\in\mathbb{R}.\ $

$(x-y)(f(f(x)^2)-f(f(y)^2))=(f(x)-f(y))(f(x)^2-f(y)^2$

Functional equation for cosine on $[0,\frac{\pi}{2}]$

Does this functional equation have a solution (also is there free functional equation solving software)?

Find $f$ such that $xf(x)+x^2f(x-1)=f(x^2)$

A functional equation problem: $f(f(x))=x^2-x+1$

Find all functions $f:\mathbb{N}\rightarrow\mathbb{N}$ such that $\gcd(f(m),n) + \text{lcm}(m,f(n)) = \text{lcm}(f(m),n) + \gcd(m,f(n))$

Solve a parametered function equation

How many functions respect the equation $3f(f(x))-7f(x)+2x=0$

Does there exist a non-constant solution to this (and other similar) functional equations?

Why doesn't solving this functional equation in this way work?

Find all functions $f:\mathbb R \rightarrow \mathbb R$ such that $x^2\cdot f(x)+f(1-x)=2x-x^4$ $\forall\; x\in \mathbb R$

If $d(x, y) = |f(x) - f(y)|$ is invariant under reflections of the real line, can we deduce $d(x, y) = \alpha |x-y|$?

Find all functions $f: \mathbb R \rightarrow \mathbb R$ such that $f(xf(x)+f(y))=(f(x))^2+y$ $\; \forall \; x,y \; \in \mathbb R$

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