# Questions tagged [even-and-odd-functions]

Even functions have reflective symmetry across the $y$-axis; odd functions have rotational symmetry about the origin.

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### Question on even, odd complex valued function

I was solving following multiple choice question (more than one options may be correct) on complex analysis. Question: The function $f(z)=z^2$ where $0 \leq \arg(z) \leq \pi$ is not (a) even (b) odd (...
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### Why is the decomposition of a function into odd and even parts interesting?

For all functions $f:\mathbb{R}\to\mathbb{R}$ one can find a unique decomposition $f(x)=E(x)+O(x)$ where $E(-x)=E(x)$ and $O(-x)=-O(x)$. Is there any branch of mathematics where analysing the ...
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### Do functions over a ring have an odd and an even part?

All functions $f(x):\mathbb{R}\to\mathbb{R}$ can be decomposed into an even and an odd part $f(x)=E(x)+O(x)$. The proof I see here, and on Wikipedia requires $2$ to have an inverse, however I want to ...
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### Is $y^2$ an even function?

yesterday I asked this question the solution of this problem says that since $y^2$ is an even function and so is $cosx-1$ therefore $y'$ is an even function which implies $y$ is odd function and from ...
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### Is $y^2$ even function??

the solution of this problem says that since $y^2$ is an even function and so is $cosx-1$ therefore $y'$ is an even function which implies $y$ is odd function and from there on the solution builds up ...
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### Error in the notes about even/odd function?

Exercise: Be $f,g: \mathbb{R}\to\mathbb{R}$ two functions. $f$ is odd, and $g$ is even. Prove that $f(g(x))$ is odd, and $g(f(x))$ is even. I personally think there is a mistake since both the ...
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### Integration of odd and even functions. Where is a flaw in my proof?

If the function $f$ has the property $f(a+x) = -f(a-x)$ $\forall x$, where a is a constant, then $$\int_{(a-2)}^{(a+2)} f(x)dx = 0$$. I have to deside whether this statement is true or false, and ...
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