Prove that if an even function $f(x)$ is $C^2$, $f(|x|)$ is also $C^2$
134439
Proving function is $C^k$
72694
Proving that $f(x) = g(x)$ for some $x \in [a,b]$ if $f,g$ continuous, $f(a)  g(b)$
139744
For a continuous function $f$ show $\exists c\in (0,1)$ s.t $f(c)=3c^2$
64905
Let $f \in C [a,b]$ such that $\forall x\exists y$ such that $|f(y)| \leq \frac{1}{2}|f(x)|$. Prove that $\exists c\in [a,b]$ such that $f(c) = 0$.
81921
If $f(x + y) = f(x) + f(y)$ showing that $f(cx) = cf(x)$ holds for rational $c$
61640
Prove c exists for f:[0,1] -> R
117418
Showing that the image of a function is $\mathbb{C}$ if it satisfies a nice functional equation
5419
Continuous functions with $f^2(x)=g^2(x)\neq 0$
39230
Even function has even sequences of polynomials converging uniformly?
103706
If $\{f(0)\}^{2} + \{f'(0)\}^{2} = 4$ then there is a $c$ with $f(c) + f''(c) = 0$
97643
Prove that:$f(f(x)) = x^2 \implies \int_{0}^{1}{(f(x))^2dx} \geq \frac{3}{13}$
13270
Prove $\exists \xi \in (a,b):f'(\xi)<1+f^2(\xi)$
11158
Proof that a continuous function with $f(x) = f(x^2)$ is constant.
45602
Show that is $\int_A f$ exists, then so does $\int_A |f|$
56413
$f(g(x))=g(f(x))$ implies $f(c)=g(c)$ for some $c$
28620
Function $f(z)$ such that $|f(z)| > |z|$ for every $z\in\mathbb{C}, 1/f(z)$
82229
Show if complex function $f(z)$ contains all real coefficients then $f(\bar z)$ = $\bar {f(z)}$