# Tagged Questions

The name "functional equation" is used for problems where the goal is to find all functions satisfying the given equation (and maybe some other conditions). So in this case, solving the equation means finding all functions fulfilling the equation. (This is different from the more common use of the ...

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### A matrix version of Fredholm integral equation of the second kind

Fredholm integral equation are often encountered in physics. I have to deal with the following Fredholm matrix equation \big[ L (x,y) \big]_{ij} = \big[ A (x,y) \big]_{ij} + \sum_{k} \...
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### Find $f(2)$ if $f$ satisfies $2f(x)-3f(\frac1x)=x^2$

The following expression is given, and we are asked to find $f(2)$. $$2f(x)-3f\left(\frac{1}{x}\right) =x^2$$ Does a unique and well defined answer exist? Why? and what ...
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### Determine all functions (functional equation) [closed]

Determine all functions $f : \mathbb{R} \to \mathbb{R}$ that satisfy the functional equation $$f(x + y) + f(z) = f(x) + f(y + z)$$ for all $x, y, z \in \mathbb{R}$.
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### Find value of a functional equation

Find $f(x)$ such that $$2 f(n) + \frac{1}{3}f\left(\frac{1}{n}\right) = 12.$$ Can anybody suggest me a way to solve this kind of functional equations?
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### Periodic Function With A Given Functional Equation

Let $f$ be a real valued function defined for all real numbers $x$ such that for some positive constant '$a$' the equation $f(x+a)=1/2+\sqrt{f(x)-(f(x))^2}$ holds for all $x$. Then prove that $f$ is ...
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### Function preserving exponentiation [duplicate]

I'm wondering what kind of function preserves exponentiation, i.e., what is an $f$ such that $f(a^b)=f(a)^{f(b)}$?
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### Polynomial equation $f(x)f(2x^2)=f(2x^3+x)$

Find all polynomials $f(x)$, for which $f(x)f(2x^2)=f(2x^3+x)$. I have no idea how to do it.
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### Role of functional equations in current panorama of pure mathematics

It seems that currently functional equations are greatly explored as a research field. I would like to know what is the importance and role of such a field in the panorama of the current development ...
### Entire $f,g$ such that $f(f(z)) = p(g(z))$
Let $p(z)$ be a given polynomial of degree $3$. How to find nonconstant entire functions $f,g$ such that $f(f(z)) = p(g(z))$ or prove they do not exist ? I considered the related equation \$f(f(z)) ...