Question

Given $f(x+1/x) = x^2 +1/x^2$, find $f(x)$

score 30.8k · Answer 1 · 2012-10-25 16:01:28

30.8k

Views

Given $f(x+1/x) = x^2 +1/x^2$, find $f(x)$

Published on 25 Oct 2012 - 16:01

score 1.2k · Answer 2 · 2012-10-26 01:46:49

1.2k

Views

Find all positive functions of a positive real such that $ f(xf(y))=yf(x) $ and $\lim_{x\to\infty}f(x)=0$

Published on 26 Oct 2012 - 1:46

score 145 · Answer 3 · 2026-03-29 14:58:49

145

Views

How many ways to reach $1$ from $n$ by doing $/13$ or $-7$?

Published on 29 Mar 2026 - 14:58

score 306 · Answer 4 · 2026-04-11 07:16:35

306

Views

A functional equation: $f(x, y + z) = f(x, y) + f(x + y, z)$

Published on 11 Apr 2026 - 7:16

score 4k · Answer 5 · 2012-11-06 10:54:50

4k

Views

Given $f(f(x))$ can we find $f(x)$?

Published on 06 Nov 2012 - 10:54

score 342 · Answer 6 · 2026-04-10 23:17:13

342

Views

Is there a non-constant function $f:\mathbb{R}^2 \to \mathbb{Z}/2\mathbb{Z}$ that sums to 0 on corners of squares?

Published on 10 Apr 2026 - 23:17

score 223 · Answer 7 · 2012-11-08 12:05:05

223

Views

Find all function such that $f(x)-f(y) = (x -y)g(\sqrt{xy})$

Published on 08 Nov 2012 - 12:05

score 243 · Answer 8 · 2012-11-09 01:02:09

243

Views

Are there associative bijections $f\colon \mathbb{N} \times \mathbb{N} \to \mathbb{N}$?

Published on 09 Nov 2012 - 1:02

score 215 · Answer 9 · 2012-11-09 09:47:25

215

Views

Find all function $f$ such that $f(x)+f(\frac1x)=\frac1a; a$ is constant

Published on 09 Nov 2012 - 9:47

score 57 · Answer 10 · 2012-11-10 13:18:13

57

Views

Prove: we always have at least x>0 is a $x^3+bx^2+cx-d^2=0$ 's root

Published on 10 Nov 2012 - 13:18

score 205 · Answer 11 · 2012-11-11 12:29:19

205

Views

Find a function $f :\mathbb{R} \to \mathbb{R}$ with some conditions

Published on 11 Nov 2012 - 12:29

score 129 · Answer 12 · 2012-11-11 14:11:00

129

Views

find $f(x)$ when $3f(x-6)-2f(x-9)=x^2-54$

Published on 11 Nov 2012 - 14:11

score 195 · Answer 13 · 2012-11-14 12:19:42

195

Views

Given $2xf(x)+(x-3)f(\frac{1}{1-x})=4x^2-10x-\frac{1}{2}$, find $f(x)$.

Published on 14 Nov 2012 - 12:19

score 3.3k · Answer 14 · 2026-04-11 00:09:24

3.3k

Views

Properties of solutions of the functional equation $f(kx) = kf(x)$

Published on 11 Apr 2026 - 0:09

score 274 · Answer 15 · 2012-11-14 22:06:48

274

Views

A functional equation: $f\left(x^2-1\right)+2f\left(\frac{2x-1}{(x-1)^2}\right)=2-\frac{4}{x}+\frac{3}{x^2}$

Published on 14 Nov 2012 - 22:06

List Question

Given $f(x+1/x) = x^2 +1/x^2$, find $f(x)$

Find all positive functions of a positive real such that $ f(xf(y))=yf(x) $ and $\lim_{x\to\infty}f(x)=0$

How many ways to reach $1$ from $n$ by doing $/13$ or $-7$?

A functional equation: $f(x, y + z) = f(x, y) + f(x + y, z)$

Given $f(f(x))$ can we find $f(x)$?

Is there a non-constant function $f:\mathbb{R}^2 \to \mathbb{Z}/2\mathbb{Z}$ that sums to 0 on corners of squares?

Find all function such that $f(x)-f(y) = (x -y)g(\sqrt{xy})$

Are there associative bijections $f\colon \mathbb{N} \times \mathbb{N} \to \mathbb{N}$?

Find all function $f$ such that $f(x)+f(\frac1x)=\frac1a; a$ is constant

Prove: we always have at least x>0 is a $x^3+bx^2+cx-d^2=0$ 's root

Find a function $f :\mathbb{R} \to \mathbb{R}$ with some conditions

find $f(x)$ when $3f(x-6)-2f(x-9)=x^2-54$

Given $2xf(x)+(x-3)f(\frac{1}{1-x})=4x^2-10x-\frac{1}{2}$, find $f(x)$.

Properties of solutions of the functional equation $f(kx) = kf(x)$

A functional equation: $f\left(x^2-1\right)+2f\left(\frac{2x-1}{(x-1)^2}\right)=2-\frac{4}{x}+\frac{3}{x^2}$

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