Is there any unique function $c=f(a, b)$ such that if I know only $c$, I can deduce unique $a$ and $b$ from it?
34260
Injective function from $\mathbb{R}^2$ to $\mathbb{R}$?
54797
Find the continuous function defined over $[0,1]$ such that $\int_0^1f(x){\rm d}x=1, \int_0^1 xf(x){\rm d}x=a$ and $\int_0^1x^2f(x){\rm d}x=a^2 .$
81799
Examples of functions where $f(ab)=f(a)+f(b)$
135577
Prove the existence of $c$ such that $f'(c) = 2c(f(c) - f(0))$
29647
Do there exist functions satisfying $f(x+y)=f(x)+f(y)$ that aren't linear?
143354
Prove that there exists $c\in\mathbb{R}$ such that $f'(c)=f(c)$
92376
Let $f:A \rightarrow B$ and C ⊂A. Define f[C]={b∈B: b=f(a) for some a∈C}. Prove or disprove each of the statement
91786
Proving and disproving $\exists b,c\in \mathbb R$ such that $f(x)=\frac a2x^2+bx+c $
84143
Given any function $g(x): \mathbb{R} \rightarrow \mathbb{R}$, find a function $f(x)$ such that $f(f(x)) = g(x)$.
122329
Determine all functions $f(x)$ such that $f(f(x+y))=f(x)+f(y)$
55924
How many distinct functions can be defined from set A to B?
56413
$f(g(x))=g(f(x))$ implies $f(c)=g(c)$ for some $c$
155531
Entire functions such that $f(z+\lambda_1)=af(z) \; , \; f(z+\lambda_2)=bf(z) $
149122
If two functions are defined by the same formula, but have different codomains, are they equal?
35889
Suppose that f(0) = f(1) = 0 and x ∈ (0, 1). Prove that there exists c ∈ (0, 1) such that f'(c) = f(x).
1071
Determine all functions $f:\mathbb{N}\rightarrow\mathbb{N}$ such that $xf(y)+yf(x)=(x+y)f(x^2+y^2)$ for all $x,y\in\mathbb{N}$ (contest question)
76148
Show that $\exists c \in \mathbb{R} : f(c) = 0$