Prove: For a function $f$, if $f^2$ and $f^3$ are analytic in G (a set in C), then $f$ is analytic in C.
46514
Proving that if $f: \mathbb{C} \to \mathbb{C} $ is a continuous function with $f^2, f^3$ analytic, then $f$ is also analytic
85612
Let functions $ f: A \to B$ and $g: B \to A$, suppose that $ g \circ f = i_A$. Prove that if $f$ is onto, then $g$ is one-to-one
10727
Let $f$ be an entire function and $L$ a line in $\mathbb{C}$ such that $f(\mathbb{C})\cap L=\emptyset$. Show that $f$ is constant function.
148474
on the boundary of analytic functions
72694
Proving that $f(x) = g(x)$ for some $x \in [a,b]$ if $f,g$ continuous, $f(a)  g(b)$
19178
$f$ continuous, $f^N$ analytic on a domain D implies $f$ analytic on D
143354
Prove that there exists $c\in\mathbb{R}$ such that $f'(c)=f(c)$
50012
$f: [a,b] \to \mathbb{R}$, $f(a) = f(b)$. Show $\exists c \in [a, \frac{a+b}{2} ]$ with $f(c)=f(c+\frac{b-a}{2})$
55138
An analytic function $f$ on $\{z \in\mathbb{C} : |z|>1 \}$
50342
Proving that a Function is Analytic Given that it is Equal to the Complex Conjugate of an analytic Function
70912
If $g\circ f$ is injective and $f$ is surjective then $g$ is injective
105652
Suppose $f: \mathbb{R} \to \mathbb{R}$ is function such that $f^3$ is continuous on $\mathbb{R}$. Prove that $f$ is continuous on $\mathbb{R}$
45676
Showing that $f$ is linear function if $\forall z \in \mathbb{C}$, $|f(z)| \leq 1 + |z|$.
125566
The Identity Theorem for real analytic functions
46629
Prove if $f(x) = g(x)$ for each rational number x and $f$ and $g$ are continuous, then $f = g$
149399
Given continuous $f$ and $g$, there exists $c \in (a,b)$ such that $\int_{a}^{c} f(x) \ \mathrm dx = \int_{c}^{b} g(x) \ \mathrm dx$
40604
Is this proof correct for : Does $F(A)\cap F(B)\subseteq F(A\cap B) $ for all functions $F$?