List questions from even-and-odd-functions

Published on 28 Dec 2023 - 0:01

74

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$f(f(x)) = x^3$, can $f$ be proved to be an odd function

Published on 10 Jan 2024 - 19:29

183

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For which polynomials $f$ does there exist a $g$ with $g\circ f$ even?

Published on 07 Feb 2024 - 22:17

36

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Claims about solution of nonlinear differential equation with symmetries

Published on 08 Feb 2024 - 1:09

85

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Let $F(x)= \int_{0}^{x} f(t) \, dt$. Show that if f is even, F is odd.

Published on 11 Feb 2024 - 15:34

11

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Parity of solutions to the Abel equation of the second kind $yp-y=f(x)$ for even and odd $f(x)$

Published on 23 Feb 2024 - 19:53

66

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Proving the derivative of an even function is odd using the chain rule

Published on 04 Mar 2024 - 12:38

43

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generating function, compositions odd, congruence modulo

Published on 05 Mar 2024 - 17:24

42

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Even function given a condition

Published on 08 Mar 2024 - 11:45

1.4k

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Continuous even functions closed and dense

Published on 04 May 2015 - 5:12

3k

Views

How to show that an odd function always goes through zero?

Published on 14 Dec 2015 - 16:15

318

Views

If $f$ is continuous and $\int^{a}_{-a} f(x) \,dx=0$, is $f$ necessarily odd?

Published on 20 Apr 2017 - 11:42

219

Views

Improper Integral - Odd Function and Symmetric range but Diverge

Published on 30 Jun 2017 - 6:22

2.8k

Views

Is $\sqrt{x}$ an even function?

Published on 23 Aug 2017 - 16:10

1.8k

Views

Odd extension of function

Published on 13 Sep 2017 - 12:34

List Question

best polynomial approximations to $f$ vanish at $0$ imply $f$ is an odd function

$f(f(x)) = x^3$, can $f$ be proved to be an odd function

For which polynomials $f$ does there exist a $g$ with $g\circ f$ even?

Claims about solution of nonlinear differential equation with symmetries

Let $F(x)= \int_{0}^{x} f(t) \, dt$. Show that if f is even, F is odd.

Parity of solutions to the Abel equation of the second kind $yp-y=f(x)$ for even and odd $f(x)$

Proving the derivative of an even function is odd using the chain rule

generating function, compositions odd, congruence modulo

Even function given a condition

Continuous even functions closed and dense

How to show that an odd function always goes through zero?

If $f$ is continuous and $\int^{a}_{-a} f(x) \,dx=0$, is $f$ necessarily odd?

Improper Integral - Odd Function and Symmetric range but Diverge

Is $\sqrt{x}$ an even function?

Odd extension of function

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