Question

How find all the functions which satisfy the functional equation $f(a+x)-f(a-x)=4ax$?

score 169 · Answer 1 · 2020-05-05 16:15:39

169

Views

How find all the functions which satisfy the functional equation $f(a+x)-f(a-x)=4ax$?

Published on 05 May 2020 - 16:15

score 400 · Answer 2 · 2020-05-05 16:41:13

400

Views

Find all strictly monotone $f:(0,+\infty) \to (0, +\infty)$ such that $f(\frac{x^2}{f(x)})=x.$

Published on 05 May 2020 - 16:41

score 137 · Answer 3 · 2020-05-05 20:45:55

137

Views

To find all functions $f: (0,\infty) \rightarrow (0, \infty)$ such that $f(x+y) = f(x)f(yf(x))$

Published on 05 May 2020 - 20:45

score 122 · Answer 4 · 2020-05-06 16:17:12

122

Views

Find all function $f : \mathbb{R} \to \mathbb{R}$ s.t. $\lim_{x \to 0} \frac{f(x)}{x}=1$ & $f(x+y)=f(x)+f(y)+2xy$.

Published on 06 May 2020 - 16:17

score 100 · Answer 5 · 2020-05-06 19:24:36

100

Views

Functional logarithmic equation: $\ln\left(\int_1^2f(x)\,\mathrm{d}x\right)=\int_1^2 \ln f(x)\,\mathrm{d}x$

Published on 06 May 2020 - 19:24

score 98 · Answer 6 · 2020-05-07 08:09:31

98

Views

$f:\mathbb Q\to\mathbb C$ satisfying $f(x_1+\dots+x_{1988})=f(x_1)\dots f(x_{1988})$ and $\overline{f(1988)}f(x)=f(1988)\overline{f(x)}$

Published on 07 May 2020 - 8:09

score 186 · Answer 7 · 2020-05-07 17:38:37

186

Views

How to prove that whether it is a Banach space or not?

Published on 07 May 2020 - 17:38

score 63 · Answer 8 · 2026-03-29 03:28:30

63

Views

What is the geometrical meaning of the space?

Published on 29 Mar 2026 - 3:28

score 179 · Answer 9 · 2020-05-08 10:48:17

179

Views

Solving a functional equation in CDF's of probability distributions

Published on 08 May 2020 - 10:48

score 273 · Answer 10 · 2020-05-08 13:20:22

273

Views

Find a formula for $g(x)$ satisfying given conditions

Published on 08 May 2020 - 13:20

score 200 · Answer 11 · 2026-03-30 08:13:47

200

Views

Number of solutions to a functional equation

Published on 30 Mar 2026 - 8:13

score 71 · Answer 12 · 2020-05-09 20:03:31

71

Views

Functional equation polynomial problem: $x^2f(x-1)=(x-1)^2f(x)$

Published on 09 May 2020 - 20:03

score 351 · Answer 13 · 2020-05-10 04:03:26

351

Views

Determine all $f : \mathbb R \rightarrow \mathbb R$ such that $f(f(x) + y) = f(x^2 - y) + 4yf(x)$.

Published on 10 May 2020 - 4:03

score 122 · Answer 14 · 2020-05-10 05:43:47

122

Views

Determine all $f : \mathbb R \rightarrow \mathbb R$ such that $f(x^3 + y^3) = x^2f(x) + yf(y^2)$.

Published on 10 May 2020 - 5:43

score 110 · Answer 15 · 2026-03-25 19:00:15

110

Views

Solving Functional Equation Involving Substitution

Published on 25 Mar 2026 - 19:00

List Question

How find all the functions which satisfy the functional equation $f(a+x)-f(a-x)=4ax$?

Find all strictly monotone $f:(0,+\infty) \to (0, +\infty)$ such that $f(\frac{x^2}{f(x)})=x.$

To find all functions $f: (0,\infty) \rightarrow (0, \infty)$ such that $f(x+y) = f(x)f(yf(x))$

Find all function $f : \mathbb{R} \to \mathbb{R}$ s.t. $\lim_{x \to 0} \frac{f(x)}{x}=1$ & $f(x+y)=f(x)+f(y)+2xy$.

Functional logarithmic equation: $\ln\left(\int_1^2f(x)\,\mathrm{d}x\right)=\int_1^2 \ln f(x)\,\mathrm{d}x$

$f:\mathbb Q\to\mathbb C$ satisfying $f(x_1+\dots+x_{1988})=f(x_1)\dots f(x_{1988})$ and $\overline{f(1988)}f(x)=f(1988)\overline{f(x)}$

How to prove that whether it is a Banach space or not?

What is the geometrical meaning of the space?

Solving a functional equation in CDF's of probability distributions

Find a formula for $g(x)$ satisfying given conditions

Number of solutions to a functional equation

Functional equation polynomial problem: $x^2f(x-1)=(x-1)^2f(x)$

Determine all $f : \mathbb R \rightarrow \mathbb R$ such that $f(f(x) + y) = f(x^2 - y) + 4yf(x)$.

Determine all $f : \mathbb R \rightarrow \mathbb R$ such that $f(x^3 + y^3) = x^2f(x) + yf(y^2)$.

Solving Functional Equation Involving Substitution

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