Show the following continuous function has a solution $f(c) = 0$
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 $f(c) = 0$.
100740
proof of that a continuous function has a fixed point
117418
Showing that the image of a function is $\mathbb{C}$ if it satisfies a nice functional equation
158888
Prove that the function $f(x)=\frac{x}{x^2+1}$ is continuous at $x=-1$.
80643
Show that f(x) defined on [0,infinity) R to is continuous at 0.
55210
Prove that the equation: $c_0+c_1x+\ldots+c_nx^n=0$ has a real solution between 0 and 1.
99179
Continuous function with compact domain has continuous inverse
61640
Prove c exists for f:[0,1] -> R
151410
Inequality of continuous functions
46834
show that a distance function is continuous
141223
$f(x^2) = 2f(x)$ and $f(x)$ continuous
101700
Liouvilles theorem question - show $f$ is constant
35889
Suppose that f(0) = f(1) = 0 and x ∈ (0, 1). Prove that there exists c ∈ (0, 1) such that f'(c) = f(x).
34719
Show this holomorphic function is constant
150554
proof that $f'$ is continuous at $a$
71049
Functional equation $f(xy)=f(x)+f(y)$ and continuity
44607
Prove that a continuous function on a closed interval attains a maximum