What let's us do stuff like $F(a) = F(b)$ for $a=b$?
47135
Prove if a = b, then f(a) = f(b) for any function f (with natural deduction)
122329
Determine all functions $f(x)$ such that $f(f(x+y))=f(x)+f(y)$
31698
$f(m^2 + f(n)) = f(m)^2 + n$ for all natural numbers
82597
How to find $ f(x)$ if $f(1-f(x))=x$ for all $x$ $\in \mathbb{R}$
97184
Show: $ f(a) = a,\ f(b) = b \implies \int_a^b \left[ f(x) + f^{-1}(x) \right] \, \mathrm{d}x = b^2 - a^2 $
72694
Proving that $f(x) = g(x)$ for some $x \in [a,b]$ if $f,g$ continuous, $f(a)  g(b)$
113804
Why does $F=ma$? Is there a straightforward reason?
47856
$f(x)=ax+b$ for some $a,b\in\mathbb{Q}$ if $f(\mathbb{Q})\subset\mathbb{Q}$ and $f(\mathbb{R-Q})\subseteq \mathbb{R}-\mathbb{Q}$
89257
Give an example of a function $f:\mathbb{R}^2 \mapsto \mathbb{R}^2$ such that
32575
What's the name for the property of a function $f$ that means $f(f(x))=x$?
145507
Is $K[a,b]=K(a,b)$ for algebraic $a, b$?
1394
How do we know that $F = ma$, not $F = k \cdot ma$
86128
Find all functions $ f : \Bbb R \to \Bbb R$ which satisfy $f(x)f(y) = f(x + y) + xy$ for all $x, y ∈ \Bbb R$.
122160
$f:\mathbb R \to \mathbb R$ be a continuous such that $f(f(f(x)))=x,\forall x \in \mathbb R$ , is $f(x)=x , \forall x \in \mathbb R$?
146152
Characterising functions $f$ that can be written as $f = g \circ g$?
83894
$f(x^2) = xf(x)$ implies that $ f(x) = mx$?
81720
$f(x) + f(x+f(y)) = y + f(f(x) + f(f(y)))$