Question

How to Solve Composite Trigonometric Functional equation

score 26 · Answer 1 · 2026-04-09 02:41:06

26

Views

How to Solve Composite Trigonometric Functional equation

Published on 09 Apr 2026 - 2:41

score 72 · Answer 2 · 2026-04-17 08:19:30

72

Views

Solution to equation $\psi(x)-2\psi(\frac{x}{2})+ \psi (\frac{x}{4}) = x^2$ with $\psi(0)=1$.

Published on 17 Apr 2026 - 8:19

score 26 · Answer 3 · 2026-04-10 10:45:26

26

Views

Finding a linear relationship between functions?

Published on 10 Apr 2026 - 10:45

score 171 · Answer 4 · 2026-04-17 04:39:49

Find all odd functions $f:\mathbb R\to\mathbb R$ that satisfy $f(x+1)=f(x)+1$ and $f\left(\frac{1}{x}\right)=\frac{f(x)}{x^2}$

score 281 · Answer 5 · 2026-04-17 17:05:15

281

Views

Finding all functions $f:\mathbb{R}\to\mathbb{R}$ such that $f\bigl(xf(x+y)\bigr)=f\bigl(yf(x)\bigr)+x^2$

Published on 17 Apr 2026 - 17:05

score 300 · Answer 6 · 2026-04-16 11:51:37

300

Views

Find all surjective functions $f(x+f(y))+f(y+f(x))=f(f(2x)+2y)$

Published on 16 Apr 2026 - 11:51

score 37 · Answer 7 · 2026-04-15 21:32:53

37

Views

Determining all real functions $g=\frac{y}{x}$, where $y$ is an involution

Published on 15 Apr 2026 - 21:32

score 332 · Answer 8 · 2026-04-14 20:29:10

332

Views

Given $f(xy)=xf(y)+yf(x)$ and $f(x+y)=f(x^{2021})+f(y^{2021})$. Calculate $f(\sqrt{2020})$

Published on 14 Apr 2026 - 20:29

score 44 · Answer 9 · 2026-04-16 05:42:45

44

Views

Finding function according to the conditions $ x f ( x ) + 2 > 0 $ and $ f ( x ) f \left( f ( x ) + \frac 4 x \right) = 1 $

Published on 16 Apr 2026 - 5:42

score 520 · Answer 10 · 2026-04-13 23:30:36

520

Views

Functional equation $f(px)+p=[f(x)]^2$

Published on 13 Apr 2026 - 23:30

score 398 · Answer 11 · 2026-04-16 10:37:12

398

Views

A function satisfying $f(x+y)+f(x-y)=2f(x)f(y)$ and $f(x_0)=-1$ is periodic

Published on 16 Apr 2026 - 10:37

score 294 · Answer 12 · 2026-04-14 05:21:53

294

Views

Trying to understand pathological solution(s) to $f:f\rightarrow f$

Published on 14 Apr 2026 - 5:21

score 280 · Answer 13 · 2026-04-16 20:23:42

280

Views

If $f(x) + 3x^2 = 2f(1-x)$ and $\lim _{x\to 1}f(x) =7$, find $\lim _{x\to 0} f(x)$.

Published on 16 Apr 2026 - 20:23

score 133 · Answer 14 · 2026-04-17 04:45:33

Finding all functions $f:\mathbb R\to\mathbb R$ that satisfy $f\left(f(x)-y^2\right)=f\left(x^2\right)+y^2f(y)-2f(xy)$, $\forall x\in\mathbb R$

score 259 · Answer 15 · 2026-04-16 16:22:20

259

Views

Find all functions that satisfy the condition $f(xy,\frac{x}{y})=x^{2}-y^{2}$

Published on 16 Apr 2026 - 16:22

List Question

How to Solve Composite Trigonometric Functional equation

Solution to equation $\psi(x)-2\psi(\frac{x}{2})+ \psi (\frac{x}{4}) = x^2$ with $\psi(0)=1$.

Finding a linear relationship between functions?

Find all odd functions $f:\mathbb R\to\mathbb R$ that satisfy $f(x+1)=f(x)+1$ and $f\left(\frac{1}{x}\right)=\frac{f(x)}{x^2}$

Finding all functions $f:\mathbb{R}\to\mathbb{R}$ such that $f\bigl(xf(x+y)\bigr)=f\bigl(yf(x)\bigr)+x^2$

Find all surjective functions $f(x+f(y))+f(y+f(x))=f(f(2x)+2y)$

Determining all real functions $g=\frac{y}{x}$, where $y$ is an involution

Given $f(xy)=xf(y)+yf(x)$ and $f(x+y)=f(x^{2021})+f(y^{2021})$. Calculate $f(\sqrt{2020})$

Finding function according to the conditions $ x f ( x ) + 2 > 0 $ and $ f ( x ) f \left( f ( x ) + \frac 4 x \right) = 1 $

Functional equation $f(px)+p=[f(x)]^2$

A function satisfying $f(x+y)+f(x-y)=2f(x)f(y)$ and $f(x_0)=-1$ is periodic

Trying to understand pathological solution(s) to $f:f\rightarrow f$

If $f(x) + 3x^2 = 2f(1-x)$ and $\lim _{x\to 1}f(x) =7$, find $\lim _{x\to 0} f(x)$.

Finding all functions $f:\mathbb R\to\mathbb R$ that satisfy $f\left(f(x)-y^2\right)=f\left(x^2\right)+y^2f(y)-2f(xy)$, $\forall x\in\mathbb R$

Find all functions that satisfy the condition $f(xy,\frac{x}{y})=x^{2}-y^{2}$

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