Question

given that $h$ is differentiable and $h(3x)+h(2x)+h(x) = 0$ for all $x\in\mathbb{R},$ is $h$ necessarily identically zero?

score 361 · Answer 1 · 2026-04-11 00:39:33

361

Views

given that $h$ is differentiable and $h(3x)+h(2x)+h(x) = 0$ for all $x\in\mathbb{R},$ is $h$ necessarily identically zero?

Published on 11 Apr 2026 - 0:39

score 117 · Answer 2 · 2026-04-16 09:22:27

117

Views

Defined function $f:\mathbb{R} \to \mathbb{R}$ which satisfies $f(2xy) + f(f(x + y)) + f(x + y) = xf(y) + yf(x)$

Published on 16 Apr 2026 - 9:22

score 211 · Answer 3 · 2026-04-15 21:52:37

211

Views

Solving functional equations with antiderivatives as input : $f(F^{-1}(x)) = 1 - \frac{1}{f(x)}$

Published on 15 Apr 2026 - 21:52

score 76 · Answer 4 · 2026-04-09 11:29:44

76

Views

Functional Equation and Definite Integral Combo

Published on 09 Apr 2026 - 11:29

score 156 · Answer 5 · 2026-04-15 23:41:14

156

Views

compute $\int_0^1 f(x)dx$

Published on 15 Apr 2026 - 23:41

score 77 · Answer 6 · 2026-04-15 21:21:03

77

Views

Functional equation $f:\Bbb{R} \to \Bbb{R}, f(xf(y)+y)=yf(x)+f(y)$

Published on 15 Apr 2026 - 21:21

score 164 · Answer 7 · 2026-04-15 14:47:50

164

Views

If $f(x + y) = f(x) + f(y) +xy$ and $f(4) = 10$ then $f(2001) = ?$ Why is my answer wrong?

Published on 15 Apr 2026 - 14:47

score 91 · Answer 8 · 2026-04-14 18:14:14

91

Views

Functional equation $f(y)f(x+f(y))=f(xy)+f(y)^2.$

Published on 14 Apr 2026 - 18:14

score 167 · Answer 9 · 2026-04-15 15:03:50

167

Views

Finding $\Bbb{R}\to \Bbb{R}$ functions satisfying $f(x + y) = f(x) + f(y)$ and $f(xy) = f(x) f(y)$

Published on 15 Apr 2026 - 15:03

score 88 · Answer 10 · 2026-04-14 19:44:20

88

Views

Determine all functions $f:\mathbb{R}\to \mathbb{R}$ so that for every pair of real numbers $x$ and $y, f(x+y^2) = f(x)+|yf(y)|$

Published on 14 Apr 2026 - 19:44

score 356 · Answer 11 · 2026-04-15 20:34:44

356

Views

functional equation $f(xf(y)) + f(yf(x)) = 1 + f(x + y)$

Published on 15 Apr 2026 - 20:34

score 372 · Answer 12 · 2026-04-11 08:29:15

372

Views

Integral In Ramanujan's Letter To G.H. Hardy

Published on 11 Apr 2026 - 8:29

score 364 · Answer 13 · 2026-04-16 13:09:34

364

Views

Prove or disprove that $f$ is a polynomial if $f(a+x)-f(x)$ is a polynomial for each fixed $a$

Published on 16 Apr 2026 - 13:09

score 150 · Answer 14 · 2026-04-14 13:13:54

150

Views

Non-reflexive space with reflexive dual space

Published on 14 Apr 2026 - 13:13

score 134 · Answer 15 · 2026-04-16 16:36:49

134

Views

To prove $f$ is Injective where $f$ satisfies $f\left(\frac{f(x)}{x}+y\right)=1+f(y)$

Published on 16 Apr 2026 - 16:36

List Question

given that $h$ is differentiable and $h(3x)+h(2x)+h(x) = 0$ for all $x\in\mathbb{R},$ is $h$ necessarily identically zero?

Defined function $f:\mathbb{R} \to \mathbb{R}$ which satisfies $f(2xy) + f(f(x + y)) + f(x + y) = xf(y) + yf(x)$

Solving functional equations with antiderivatives as input : $f(F^{-1}(x)) = 1 - \frac{1}{f(x)}$

Functional Equation and Definite Integral Combo

compute $\int_0^1 f(x)dx$

Functional equation $f:\Bbb{R} \to \Bbb{R}, f(xf(y)+y)=yf(x)+f(y)$

If $f(x + y) = f(x) + f(y) +xy$ and $f(4) = 10$ then $f(2001) = ?$ Why is my answer wrong?

Functional equation $f(y)f(x+f(y))=f(xy)+f(y)^2.$

Finding $\Bbb{R}\to \Bbb{R}$ functions satisfying $f(x + y) = f(x) + f(y)$ and $f(xy) = f(x) f(y)$

Determine all functions $f:\mathbb{R}\to \mathbb{R}$ so that for every pair of real numbers $x$ and $y, f(x+y^2) = f(x)+|yf(y)|$

functional equation $f(xf(y)) + f(yf(x)) = 1 + f(x + y)$

Integral In Ramanujan's Letter To G.H. Hardy

Prove or disprove that $f$ is a polynomial if $f(a+x)-f(x)$ is a polynomial for each fixed $a$

Non-reflexive space with reflexive dual space

To prove $f$ is Injective where $f$ satisfies $f\left(\frac{f(x)}{x}+y\right)=1+f(y)$

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