Which polynomial functions can satisfy $f(x)\cdot f({1\over x}) = f(x) + f({1\over x})$?
126931
Find $f(x)$ such that $f(x)+f\left(\frac{1}{x}\right)=f(x)\cdot f\left(\frac{1}{x}\right)$
82597
How to find $ f(x)$ if $f(1-f(x))=x$ for all $x$ $\in \mathbb{R}$
139614
Polynomial bounded real part of an entire function
24810
Functions satisfying $(b-a)f'(\tfrac{a+b}{2}) = f(b)- f(a)$
409
functions satisfying $f(x - y) = f(x) f(y) - f(a - x) f(a + y)$ and $f(0)=1$
103340
Show that this entire function is polynomial.
7199
Suppose that $P(x)$ is a polynomial of degree $n$ such that $P(k)=\dfrac{k}{k+1}$ for $k=0,1,\ldots,n$. Find the value of $P(n+1)$
65548
Prove if f(z) is entire function s.t $|f(z)|\leq M|z|$ then $f(z)$ Is polynomial of degree $1$
134699
Can *any* real polynomial be factored linearly (plus a constant) over $\mathbb{R}$?
29647
Do there exist functions satisfying $f(x+y)=f(x)+f(y)$ that aren't linear?
111756
How do I prove that then $f(x) = 1$ for some $x ∈ [0, 1]$?
37976
Find all functions $f$ such that $(x+y)f(x)+f(y^2)=(x+y)f(y)+f(x^2)$
4885
Polynomials with integer coefficients such that $p(a)=b,p(b)=c,p(c)=a$
69734
how to find all functions such that $f\left( x^{2} - y^{2} \right) = ( x - y )( f(x) + f(y) )$
14277
Proving $f(x)=x\cdot |x|$ is a bijection
132093
Solve $f(f(x))=f(x)$
118916
How do I prove that a polynomial F[x] of degree n has at most n roots