Show that $f(x)=\alpha x$ for some $\alpha \in R$
37966
If $f$ is continuous and $f(x+y) = f(x)+f(y)$, then $f(x) = cx$ for all $x \in \mathbb{R}$
28399
Showing $f$ is constant
24466
Prove that if $[F(\alpha):F]$ is odd then $F(\alpha)=F(\alpha^2)$
149564
Showing that a function is in $L^1$
18950
Show that $f$ has at most one fixed point
21891
If $f(xy)=f(x)f(y)$ then show that $f(x) = x^t$ for some t
101778
Show that there is $\eta\in(0,1)$ with $f''(\eta)=f(\eta)$
136842
$|x-f(x)|<5777$, Show that $f$ is surjective
129443
$f(\theta) = \cos \theta - \sqrt{3}\sin \theta$ in the form $r\sin(\theta-\alpha)$
24785
How prove this equation $\alpha=\aleph_{0}\alpha$
28007
Assuming: $\forall x \in [0,1]:f(x) > x$ Prove: $\forall x \in [0,1]:f(x) > x + \varepsilon $
102553
How to show that $f(z) = f(i)$
59063
$f(f(x))=f(x)$ question
8913
Show that there is $\xi$ s.t. $f(\xi)=f\left(\xi+\frac{1}{n}\right)$
2072
Demonstrate that if $f$ is surjective then $X = f(f^{-1}(X))$
72694
Proving that $f(x) = g(x)$ for some $x \in [a,b]$ if $f,g$ continuous, $f(a)  g(b)$
111186
Proving that if $|f''(x)| \le A$ then $|f'(x)| \le A/2$