Question

General form of this integral functional equation?

score 246 · Answer 1 · 2026-04-12 14:38:05

246

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General form of this integral functional equation?

Published on 12 Apr 2026 - 14:38

score 375 · Answer 2 · 2026-04-15 13:07:35

375

Views

Looking for function which satisfies $f(n)=f(2n)+f(2n+1)$

Published on 15 Apr 2026 - 13:07

score 108 · Answer 3 · 2026-04-16 02:30:00

108

Views

Find all functions $f:\mathbb{R} \to \mathbb{R},$ which is continuous in $\mathbb{R}$ then $f(x-y)+f(y-z)+f(z-x)+27=0.$

Published on 16 Apr 2026 - 2:30

score 143 · Answer 4 · 2026-04-17 07:52:42

143

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Find all functions $f:\mathbb{R} \to \mathbb{R},$ which is continuous in $\mathbb{R}$ then $f(x)=f(x^2+1).$

Published on 17 Apr 2026 - 7:52

score 81 · Answer 5 · 2026-04-15 18:00:03

Find all functions $f:\mathbb{R} \to \mathbb{R},$ which are continuous in $\mathbb{R}$ and satisfy $f(x-y)f(y-z)f(z-x)+27=0.$

score 69 · Answer 6 · 2026-04-16 22:54:49

69

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Find the continuous function that satisfies $f(x+1) + 3x^2 + 5x = f(2x+1), \forall x \in \mathbb{R}$

Published on 16 Apr 2026 - 22:54

score 48 · Answer 7 · 2026-04-17 05:31:56

48

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$f(yf^2(x))=x^3f(xy)$ for all $x,y \in {\mathbb{Q}}^{+}$

Published on 17 Apr 2026 - 5:31

score 96 · Answer 8 · 2026-04-11 19:40:46

96

Views

Solving a functional equation of type $f(x)+f(x+a)=h(x)$

Published on 11 Apr 2026 - 19:40

score 160 · Answer 9 · 2026-04-16 05:25:56

160

Views

If $f(x)$ agrees with $e^x$ on the integers, and $f(x)f(y)=f(x+y)$, then is $f(x)=e^x$?

Published on 16 Apr 2026 - 5:25

score 394 · Answer 10 · 2026-04-14 23:28:51

394

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Prove that $f(n)=n^2$ where $f$ is a strictly increasing multiplicative function with $f(2)=4$.

Published on 14 Apr 2026 - 23:28

score 125 · Answer 11 · 2026-04-15 09:20:14

125

Views

Find the values of $f(2)$ for which $f$ cannot be a strictly increasing and completely multiplicative function

Published on 15 Apr 2026 - 9:20

score 99 · Answer 12 · 2026-04-16 07:26:42

99

Views

Find all functions $f: \mathbb{N}^\to \mathbb{Z}$ satisfies $f(x+|f(y)|)=x+f(y), \forall x, y\in\mathbb{N}^$

Published on 16 Apr 2026 - 7:26

score 131 · Answer 13 · 2026-04-12 08:03:52

131

Views

Functional that leads to hollow

Published on 12 Apr 2026 - 8:03

score 326 · Answer 14 · 2026-04-17 03:52:59

Find all functions $f: \mathbb{R} \to\mathbb{R} $ such that if $a+f(b)+f^2(c) = 0$ then $f(a)^3 + bf(b)^2 + c^2f(c) = 3abc$

score 198 · Answer 15 · 2026-04-09 04:51:02

198

Views

Functional Equation Using Calculus

Published on 09 Apr 2026 - 4:51

List Question

General form of this integral functional equation?

Looking for function which satisfies $f(n)=f(2n)+f(2n+1)$

Find all functions $f:\mathbb{R} \to \mathbb{R},$ which is continuous in $\mathbb{R}$ then $f(x-y)+f(y-z)+f(z-x)+27=0.$

Find all functions $f:\mathbb{R} \to \mathbb{R},$ which is continuous in $\mathbb{R}$ then $f(x)=f(x^2+1).$

Find all functions $f:\mathbb{R} \to \mathbb{R},$ which are continuous in $\mathbb{R}$ and satisfy $f(x-y)f(y-z)f(z-x)+27=0.$

Find the continuous function that satisfies $f(x+1) + 3x^2 + 5x = f(2x+1), \forall x \in \mathbb{R}$

$f(yf^2(x))=x^3f(xy)$ for all $x,y \in {\mathbb{Q}}^{+}$

Solving a functional equation of type $f(x)+f(x+a)=h(x)$

If $f(x)$ agrees with $e^x$ on the integers, and $f(x)f(y)=f(x+y)$, then is $f(x)=e^x$?

Prove that $f(n)=n^2$ where $f$ is a strictly increasing multiplicative function with $f(2)=4$.

Find the values of $f(2)$ for which $f$ cannot be a strictly increasing and completely multiplicative function

Find all functions $f: \mathbb{N}^\to \mathbb{Z}$ satisfies $f(x+|f(y)|)=x+f(y), \forall x, y\in\mathbb{N}^$

Functional that leads to hollow

Find all functions $f: \mathbb{R} \to\mathbb{R} $ such that if $a+f(b)+f^2(c) = 0$ then $f(a)^3 + bf(b)^2 + c^2f(c) = 3abc$

Functional Equation Using Calculus

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