query: Does a function that satisfies the equality $f(a+b) = f(a)f(b)$ have to be exponential?
positive_passages.docid: 13086
positive_passages.text: Overview of basic facts about Cauchy functional equation
negative_passages.docid: 125788
negative_passages.text: A function with a property $f(x+y)=f(x)f(y)$
negative_passages.docid: 81799
negative_passages.text: Examples of functions where $f(ab)=f(a)+f(b)$
negative_passages.docid: 23465
negative_passages.text: When $f(x+1)-f(x)=f'(x)$, what are the solutions for $f(x)$?
negative_passages.docid: 145265
negative_passages.text: A non-zero function satisfying $g(x+y) = g(x)g(y)$ must be positive everywhere
negative_passages.docid: 53024
negative_passages.text: $f(x)f(1/x)=f(x)+f(1/x)$
negative_passages.docid: 86128
negative_passages.text: Find all functions $ f : \Bbb R \to \Bbb R$ which satisfy $f(x)f(y) = f(x + y) + xy$ for all $x, y ∈ \Bbb R$.
negative_passages.docid: 122329
negative_passages.text: Determine all functions $f(x)$ such that $f(f(x+y))=f(x)+f(y)$
negative_passages.docid: 22303
negative_passages.text: How do I prove that $f(x)f(y)=f(x+y)$ implies that $f(x)=e^{cx}$, assuming f is continuous and not zero?
negative_passages.docid: 99917
negative_passages.text: What function satisfies $F'(x) = F(2x)$?
negative_passages.docid: 1440
negative_passages.text: Are the any non-trivial functions where $f(x)=f'(x)$ not of the form $Ae^x$
negative_passages.docid: 28011
negative_passages.text: Does there exists an entire function such that for each $|z|>C$ for some constant $C$, $|f(z)|=|z|+1$?
negative_passages.docid: 13248
negative_passages.text: How to obtain $f(x)$, if it is known that $f(f(x))=x^2+x$?
negative_passages.docid: 122481
negative_passages.text: proof of an identity for exponential function
negative_passages.docid: 140936
negative_passages.text: If two integrals are equal, then the functions are the same
negative_passages.docid: 40047
negative_passages.text: Is $\int_a^b f(x) dx = \int_{f(a)}^{f(b)} f^{-1}(x) dx$?
negative_passages.docid: 133682
negative_passages.text: 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 $f(t)=c\cdot e^t$.