Find all functions $f: \mathbb{R}\rightarrow \mathbb{R}$ satisfying a functional equation
21891
If $f(xy)=f(x)f(y)$ then show that $f(x) = x^t$ for some t
67594
Books on functional equations
44670
Find all functions $f: \mathbb Z \to \mathbb Z$ such that $f(x+y)=f(x)+f(y)$
132488
Find all entire functions $f(z)$ such that $|f(z)|=1$ for $|z|=1$
133646
real analysis -functional equation
62966
Find all functions $f(x)$ such that $f\left(x^2+f(y)\right)$=$y+(f(x))^2$
93712
Let $f:(-1,1) \rightarrow \mathbb{R}$ be smooth on $(-1,1)$, $f(0) = 1$. Find $f(x)$.
100362
Codomain of function complete implies function space complete
61640
Prove c exists for f:[0,1] -> R
29403
Finding functions $f: \Bbb R_*^+ \to \Bbb R_*^+$ with certain properties
32599
Solution to the functional equation $f(x^y)=f(x)^{f(y)}$
117848
Find all entire functions
82597
How to find $ f(x)$ if $f(1-f(x))=x$ for all $x$ $\in \mathbb{R}$
86128
Find all functions $ f : \Bbb R \to \Bbb R$ which satisfy $f(x)f(y) = f(x + y) + xy$ for all $x, y ∈ \Bbb R$.
109942
Find continuous functions such that $f(x+y)+f(x-y)=2[f(x)+f(y)]$
57021
Is the set of all functions $f:Z_+\rightarrow Z_+$ that are eventually constant countable.
65418
Solve these functional equations: $\int_0^1\!{f(x)^2\, \mathrm{dx}}= \int_0^1\!{f(x)^3\, \mathrm{dx}}= \int_0^1\!{f(x)^4\, \mathrm{dx}}$