Is there a real-valued function $f$ such that $f(f(x)) = -x$?
11453
Find a real function $f:\mathbb{R}\to\mathbb{R}$ such that $f(f(x)) = -x$?
25010
Argue that there exists a continuous function $g: \mathbb{R} \rightarrow \mathbb{R}$ which satisfies $g(x) = \frac{1-e^{-2x^2}}{x^2}$ for $x \neq 0$
1440
Are the any non-trivial functions where $f(x)=f'(x)$ not of the form $Ae^x$
101281
Does there exist a smooth function which is nowhere analytic?
23186
$f: \mathbb{R^2} \to \mathbb{R}$ a $C^\infty$ function such that $f(x,0)=f(0,y)=0$ then exists $g$ such that $f(x,y)=xy\, g(x,y)$
111756
How do I prove that then $f(x) = 1$ for some $x ∈ [0, 1]$?
55175
Is the function $f(x) = x^2 - 2x$ one-to-one?
74810
A function $f$ such that $f' = 0$ when $x < 0$ and $f' = 1$ when $x \geq 0$?
151519
If $f(f(x))=x^2-x+1$, what is $f(0)$?
118192
Is there a bijective function $f: \mathbb{R}\to\mathbb{R}$ that is discontinuous?
144222
If $f(x + 1) + f(x − 1) = f(x), \forall x \in \mathbb{R}$,then how to find $k$ such that $f(x + k) = f(x)$?
125788
A function with a property $f(x+y)=f(x)f(y)$
44148
Functions that are their own inverse.
146152
Characterising functions $f$ that can be written as $f = g \circ g$?
2717
Help proving existence of an specific $x_0$ for which $f''(x_0)=0$
62568
Does there exists an entire function $f: \mathbb C \to \mathbb C$ which is bounded on real line and imaginary line?
122329
Determine all functions $f(x)$ such that $f(f(x+y))=f(x)+f(y)$