What happens if $f \circ f = f$ and $f$ is a real function.
106830
are $f(f(x))=f(x)$ and $f(x)=x$ equivalent?
143354
Prove that there exists $c\in\mathbb{R}$ such that $f'(c)=f(c)$
95970
Let $f:[0,1] \rightarrow \mathbb{R}$ be a continuous function. If $f(0)=f(1)$ then exists $x\in [0,1]$ s.t. $f(x) = f(x+\frac{1}{2})$
46748
If $g \circ f$ is surjective, show that $f$ does not have to be surjective?
143200
$f(r,\theta)=(r\cos\theta,r\sin\theta)$ Then
78698
Prove if $f$ has a right inverse function: $f\circ g=id_x$ $\iff$ $f$ is onto $Y$
122160
$f:\mathbb R \to \mathbb R$ be a continuous such that $f(f(f(x)))=x,\forall x \in \mathbb R$ , is $f(x)=x , \forall x \in \mathbb R$?
81921
If $f(x + y) = f(x) + f(y)$ showing that $f(cx) = cf(x)$ holds for rational $c$
80199
Do we have always $f(A \cap B) = f(A) \cap f(B)$?
21891
If $f(xy)=f(x)f(y)$ then show that $f(x) = x^t$ for some t
88201
Suppose $X$ is a finite set and $f : X \to X$ is a function. Then $f$ is injective if and only if $f$ is surjective.
103706
If $\{f(0)\}^{2} + \{f'(0)\}^{2} = 4$ then there is a $c$ with $f(c) + f''(c) = 0$
128911
Continuous extension of a real function
90565
If $f:[0,1] \rightarrow \mathbb{R}$ is continuous function such that $f(0)=f(1)$ then there exists $ x\in [0,1]$ such that $f(x) = f(x+\frac{1}{n})$.
53551
$f(A\cap B)=f(A)\cap f(B)$ $\iff$ $f$ is injective.
142873
What does the function f: x ↦ y mean?
76148
Show that $\exists c \in \mathbb{R} : f(c) = 0$