Continuous $f$ such that $f(x)=f(x^2)$ is constant?
11158
Proof that a continuous function with $f(x) = f(x^2)$ is constant.
64650
If $a\operatorname{Re}(f(z))+b\operatorname{Im}(f(z))=c$ then f is constant
127449
Uniform continuous of $f(x,y) = \sin(x^2+y)$
26388
proof that function is constant
155923
continuity of $f(x,y)$ in $\mathbb R^2$.
142494
Functions $f(x)/g(x), g(x)/h(x),h(x)/f(x)$ are constant
149399
Given continuous $f$ and $g$, there exists $c \in (a,b)$ such that $\int_{a}^{c} f(x) \ \mathrm dx = \int_{c}^{b} g(x) \ \mathrm dx$
86517
If $|f(z)|\le |g(z)|$, can we say $f$ is constant?
26754
Find all continuous functions satisfying $\int_0^xf=(f(x))^2+C$ for some constant $C \neq 0$.
148266
Let $f:X\to X $ be continuous. Does $f $ have a fixed point when $X=[0,1)$ or $X=(0,1) $?
106290
Prove a function is constant. (complex analysis)
140602
If the absolute value of an analytic function $f$ is a constant, must $f$ be a constant?
128911
Continuous extension of a real function
109896
Proving that the function $f(x,y)=\frac{x^2y}{x^2 + y^2}$ with $f(0,0)=0$ is continuous at $(0,0)$.
55368
$f$ is continuous, if $f_n$ continuous and $f_n\to f$ uniformly
62640
Show a given analytic function is constant
34940
Continuity of $f(x) = x^n$