Proof that $a^x$ is the only solution of $f(x+y)=f(x)f(y)$
125788
A function with a property $f(x+y)=f(x)f(y)$
148570
Find the all possible real solutions of $x^y=y^x$
88328
Proof of $1+x\leq e^x$ for all x?
139305
Prove $f=1+x+x^2+x^3+\cdots+x^n$ has no multiple roots.
49882
Proving $f(x,y,z)=\big(\frac{x}{a+x+y+z}, \frac{y}{a+x+y+z}, \frac{z}{a+x+y+z} \big)$ is injective
28286
About finding the function such that $f(xy)=f(x)f(y)-f(x+y)+1$
19355
prove $f(x)=x^3+x$ is one to one and onto
23465
When $f(x+1)-f(x)=f'(x)$, what are the solutions for $f(x)$?
153942
Solution of functional equation $f(x+y)=f(x)+f(y)+y\sqrt{f(x)}$
132093
Solve $f(f(x))=f(x)$
142725
The general solution of $x^a = a^x$ for real $a >0$
76679
Prove there are no other solutions of functional equation $f(x+y) = \frac{f(x)+f(y)}{1-f(x)f(y)}$
20626
Prove that $x^y < y^x$
133682
Prove that if $f(t)$ satisfies $f(t)=f'(t)$, then $f(t+s)=f(t)f(s)$ for all $t,s\in R$ without using the fact that $f(t)=c\cdot e^t$.
145368
How to show $f:Y\to X^{+}$ is continuous?
152841
I want to show that $f(x)=x.f(1)$ where $f:R\to R$ is additive.
35066
Nature and number of solutions to $xy=x+y$