Question

Prove that for any polynomial $P(x)$ there exist polynomials $F(x)$ and $G(x)$ such that $F\left(G(x) \right)-G\left(F(x) \right)=P(x)$

score 411 · Answer 1 · 2016-06-29 13:54:37

411

Views

Prove that for any polynomial $P(x)$ there exist polynomials $F(x)$ and $G(x)$ such that $F\left(G(x) \right)-G\left(F(x) \right)=P(x)$

Published on 29 Jun 2016 - 13:54

score 93 · Answer 2 · 2016-07-01 14:12:18

93

Views

Proving $(f \circ g)_{}= f_{} \circ g_{*}$

Published on 01 Jul 2016 - 14:12

score 86 · Answer 3 · 2016-07-04 13:03:47

86

Views

Is there a way to denote a repeated operation?

Published on 04 Jul 2016 - 13:03

score 1.2k · Answer 4 · 2013-04-13 12:29:49

1.2k

Views

Prove that if $Z\subseteq Y$, then $(g\circ f)^{-1}(Z)=f^{-1}(g^{-1}(Z)).$

Published on 13 Apr 2013 - 12:29

score 32 · Answer 5 · 2013-04-22 10:05:30

32

Views

Solving with composition

Published on 22 Apr 2013 - 10:05

score 2.6k · Answer 6 · 2013-04-26 05:17:58

2.6k

Views

Suppose $R$ and $S$ are transitive relations on $A$. Prove that if $S \circ R \subseteq R \circ S$ then $R \circ S$ is transitive.

Published on 26 Apr 2013 - 5:17

score 181 · Answer 7 · 2013-05-02 22:50:00

181

Views

$g(\theta):= f(\theta {\bf y} + (1 − \theta){\bf x})$, find $g'$.

Published on 02 May 2013 - 22:50

score 5.1k · Answer 8 · 2013-05-04 10:45:16

5.1k

Views

Showing that this set of functions is a group.

Published on 04 May 2013 - 10:45

score 1.1k · Answer 9 · 2013-05-06 06:15:01

1.1k

Views

Induction with compositions

Published on 06 May 2013 - 6:15

score 139 · Answer 10 · 2013-05-15 00:07:29

139

Views

Inverses where $f(g(x))=x\neq g(f(x))$

Published on 15 May 2013 - 0:07

score 131 · Answer 11 · 2026-03-26 14:34:42

131

Views

What is the functional inverse (with respect to $h$ (!)) of $f^{\circ h}(x)={F(h) +x F(h-1) \over F(1+h) +x F(h) }$?

Published on 26 Mar 2026 - 14:34

score 49 · Answer 12 · 2013-05-24 00:02:07

49

Views

Cancellation of Asymptotics

Published on 24 May 2013 - 0:02

score 112 · Answer 13 · 2013-06-04 21:55:55

112

Views

If $f:\mathbb{R} \to \mathbb{Z}$, why can't we have that $g \circ f$?

Published on 04 Jun 2013 - 21:55

score 78 · Answer 14 · 2013-06-05 13:11:54

78

Views

Question regarding finding of formulas for piecewise function composition

Published on 05 Jun 2013 - 13:11

score 175 · Answer 15 · 2013-06-07 15:47:47

175

Views

The nested self-composition of $f(x) = \frac{\sqrt3}2x+\frac12\sqrt{1-x^2}$

Published on 07 Jun 2013 - 15:47

List Question

Prove that for any polynomial $P(x)$ there exist polynomials $F(x)$ and $G(x)$ such that $F\left(G(x) \right)-G\left(F(x) \right)=P(x)$

Proving $(f \circ g)_{}= f_{} \circ g_{*}$

Is there a way to denote a repeated operation?

Prove that if $Z\subseteq Y$, then $(g\circ f)^{-1}(Z)=f^{-1}(g^{-1}(Z)).$

Solving with composition

Suppose $R$ and $S$ are transitive relations on $A$. Prove that if $S \circ R \subseteq R \circ S$ then $R \circ S$ is transitive.

$g(\theta):= f(\theta {\bf y} + (1 − \theta){\bf x})$, find $g'$.

Showing that this set of functions is a group.

Induction with compositions

Inverses where $f(g(x))=x\neq g(f(x))$

What is the functional inverse (with respect to $h$ (!)) of $f^{\circ h}(x)={F(h) +x F(h-1) \over F(1+h) +x F(h) }$?

Cancellation of Asymptotics

If $f:\mathbb{R} \to \mathbb{Z}$, why can't we have that $g \circ f$?

Question regarding finding of formulas for piecewise function composition

The nested self-composition of $f(x) = \frac{\sqrt3}2x+\frac12\sqrt{1-x^2}$

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