Question

Find all real functions that satisfy: $f(x+y) = (f(x))^2 + (f(y))^2$, $x$, $y$ $\in$ $\mathbb{R}$

score 131 · Answer 1 · 2023-03-06 07:25:10

131

Views

Find all real functions that satisfy: $f(x+y) = (f(x))^2 + (f(y))^2$, $x$, $y$ $\in$ $\mathbb{R}$

Published on 06 Mar 2023 - 7:25

score 163 · Answer 2 · 2023-03-06 16:19:16

163

Views

Solve the functional equation $\left(f(x)\right)^2 - f\left(x^2\right)=2x$

Published on 06 Mar 2023 - 16:19

score 87 · Answer 3 · 2023-03-07 15:16:58

87

Views

let $f(x)$ is polynomial function , $f(x+2)-f(x) = 6x^2+12x$ , $f(1)-f(0)=?$

Published on 07 Mar 2023 - 15:16

score 74 · Answer 4 · 2023-03-07 17:07:11

74

Views

$f(x)$ is a polynomial which satisfies $f(x)f(1/x)+5-3f(x)-3f(1/x)=0$ for all $x\in \mathbb R-\{0\}$. If $f(2)=11$, find $f(3)$.

Published on 07 Mar 2023 - 17:07

score 45 · Answer 5 · 2023-03-08 12:48:53

45

Views

A functional equation with trigonometric solution

Published on 08 Mar 2023 - 12:48

score 67 · Answer 6 · 2023-03-08 19:03:01

67

Views

Find functions $f\left(x_{1}x_{2}\right)+f\left(x_{2}x_{3}\right)+\ldots+f\left(x_{n}x_{1}\right) \ge n \cdot f\left(x_{1}+x_{2}+\ldots+x_{n}\right)$

Published on 08 Mar 2023 - 19:03

score 74 · Answer 7 · 2026-02-23 15:36:25

74

Views

Find all real function $f(x)$ satisfy the functional equation

Published on 23 Feb 2026 - 15:36

score 145 · Answer 8 · 2023-03-09 15:53:09

145

Views

Find all polynomials $f$ such that $f(x+m)=f(x)+m$

Published on 09 Mar 2023 - 15:53

score 361 · Answer 9 · 2026-03-26 01:25:12

361

Views

$f(f(z)) = z , f(\exp(z)) = \exp(f(z)) $?

Published on 26 Mar 2026 - 1:25

score 135 · Answer 10 · 2023-03-11 14:50:11

135

Views

Find the function $f(x)$ such that $f(f(x))=e^x$

Published on 11 Mar 2023 - 14:50

score 172 · Answer 11 · 2023-03-13 11:24:25

172

Views

Uniqueness of trigonometric functions from functional equation

Published on 13 Mar 2023 - 11:24

score 97 · Answer 12 · 2023-03-15 17:29:15

97

Views

When does the equations have $1,2,3$ solutions?

Published on 15 Mar 2023 - 17:29

score 39 · Answer 13 · 2026-03-25 23:50:52

39

Views

A functional that returns the function's value outside integration bounds

Published on 25 Mar 2026 - 23:50

score 114 · Answer 14 · 2023-03-22 20:00:26

114

Views

Finding a function with a functional equation.

Published on 22 Mar 2023 - 20:00

score 283 · Answer 15 · 2023-03-26 18:33:37

283

Views

Polynomial functional equation

Published on 26 Mar 2023 - 18:33

List Question

Find all real functions that satisfy: $f(x+y) = (f(x))^2 + (f(y))^2$, $x$, $y$ $\in$ $\mathbb{R}$

Solve the functional equation $\left(f(x)\right)^2 - f\left(x^2\right)=2x$

let $f(x)$ is polynomial function , $f(x+2)-f(x) = 6x^2+12x$ , $f(1)-f(0)=?$

$f(x)$ is a polynomial which satisfies $f(x)f(1/x)+5-3f(x)-3f(1/x)=0$ for all $x\in \mathbb R-\{0\}$. If $f(2)=11$, find $f(3)$.

A functional equation with trigonometric solution

Find functions $f\left(x_{1}x_{2}\right)+f\left(x_{2}x_{3}\right)+\ldots+f\left(x_{n}x_{1}\right) \ge n \cdot f\left(x_{1}+x_{2}+\ldots+x_{n}\right)$

Find all real function $f(x)$ satisfy the functional equation

Find all polynomials $f$ such that $f(x+m)=f(x)+m$

$f(f(z)) = z , f(\exp(z)) = \exp(f(z)) $?

Find the function $f(x)$ such that $f(f(x))=e^x$

Uniqueness of trigonometric functions from functional equation

When does the equations have $1,2,3$ solutions?

A functional that returns the function's value outside integration bounds

Finding a function with a functional equation.

Polynomial functional equation

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