Question

Prove that there is no function $f:\mathbb{R}^+ \rightarrow \mathbb{R}^+$ such that $f^2(x) \geq f(x+y)(f(x) + y)$

score 84 · Answer 1 · 2026-04-15 04:47:02

84

Views

Prove that there is no function $f:\mathbb{R}^+ \rightarrow \mathbb{R}^+$ such that $f^2(x) \geq f(x+y)(f(x) + y)$

Published on 15 Apr 2026 - 4:47

score 403 · Answer 2 · 2026-04-15 06:36:33

403

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Is there a function $f(x)$ that satisfies $f(e^x) = e^x f(x)$?

Published on 15 Apr 2026 - 6:36

score 92 · Answer 3 · 2026-04-11 22:10:13

92

Views

Trying to prove surjectivity

Published on 11 Apr 2026 - 22:10

score 245 · Answer 4 · 2026-04-09 21:48:24

245

Views

Replication invariance of weighted sums

Published on 09 Apr 2026 - 21:48

score 207 · Answer 5 · 2026-04-14 16:32:34

207

Views

Let $f(x+y)=2021^xf(y)+2021^yf(x)$ where $f(x)$ is continuous and $f(1)=1$. Find $f(x)$

Published on 14 Apr 2026 - 16:32

score 71 · Answer 6 · 2026-04-10 19:12:08

71

Views

Is the solution to this functional equation differentiable?

Published on 10 Apr 2026 - 19:12

score 73 · Answer 7 · 2021-05-11 10:15:21

For a function $f:\Bbb N\to\Bbb R$, the following are satisfied, (i) $f(1)=1$ and (ii) $f(1)+2f(2)+3f(3)+....+nf(n)=n(n+1)f(n).$ Find $f(n)$

score 66 · Answer 8 · 2026-04-08 17:36:20

66

Views

Finding derivative at a point from functional equation

Published on 08 Apr 2026 - 17:36

score 37 · Answer 9 · 2026-04-13 21:24:24

37

Views

Are there real functions $f(x,y)$, $g(x,y)$, such that

Published on 13 Apr 2026 - 21:24

score 145 · Answer 10 · 2026-04-13 12:50:11

145

Views

Domination of derivatives by an involution

Published on 13 Apr 2026 - 12:50

score 116 · Answer 11 · 2026-04-10 18:32:04

116

Views

Functional equation (is there a polynomial or holomorphic solution?)

Published on 10 Apr 2026 - 18:32

score 24 · Answer 12 · 2026-04-09 08:19:53

24

Views

When can we express a bivariate function in terms of a linear homomorphism?

Published on 09 Apr 2026 - 8:19

score 91 · Answer 13 · 2026-04-15 05:34:32

91

Views

Given $f : \mathbb{R} \to \mathbb{R}$ differentiable, $f(x + y) = f(x)f(y)$ and $f(0) = 1$, prove $f(x) = e^{cx}$, $c$ constant.

Published on 15 Apr 2026 - 5:34

score 204 · Answer 14 · 2021-05-23 17:17:55

Given $f: \mathbb N \to \mathbb N$ such that $2f(n)f(2n+1)=f(2n)(2f(n)+1)$ and $8f(n)>f(2n)>4(f(n)$. Find $f(12)$ in terms of $f(1)$

score 162 · Answer 15 · 2026-04-12 19:57:37

162

Views

Solutions to $\Gamma(z,1)^2 + \Gamma(z,1) = 0 $?

Published on 12 Apr 2026 - 19:57

List Question

Prove that there is no function $f:\mathbb{R}^+ \rightarrow \mathbb{R}^+$ such that $f^2(x) \geq f(x+y)(f(x) + y)$

Is there a function $f(x)$ that satisfies $f(e^x) = e^x f(x)$?

Trying to prove surjectivity

Replication invariance of weighted sums

Let $f(x+y)=2021^xf(y)+2021^yf(x)$ where $f(x)$ is continuous and $f(1)=1$. Find $f(x)$

Is the solution to this functional equation differentiable?

For a function $f:\Bbb N\to\Bbb R$, the following are satisfied, (i) $f(1)=1$ and (ii) $f(1)+2f(2)+3f(3)+....+nf(n)=n(n+1)f(n).$ Find $f(n)$

Finding derivative at a point from functional equation

Are there real functions $f(x,y)$, $g(x,y)$, such that

Domination of derivatives by an involution

Functional equation (is there a polynomial or holomorphic solution?)

When can we express a bivariate function in terms of a linear homomorphism?

Given $f : \mathbb{R} \to \mathbb{R}$ differentiable, $f(x + y) = f(x)f(y)$ and $f(0) = 1$, prove $f(x) = e^{cx}$, $c$ constant.

Given $f: \mathbb N \to \mathbb N$ such that $2f(n)f(2n+1)=f(2n)(2f(n)+1)$ and $8f(n)>f(2n)>4(f(n)$. Find $f(12)$ in terms of $f(1)$

Solutions to $\Gamma(z,1)^2 + \Gamma(z,1) = 0 $?

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