Prove that $f:X \rightarrow \mathbb{R}$ is constant.
40208
Locally Constant Functions on Connected Spaces are Constant
116056
Prove that $|f(x)-f(y)|\le|x-y|$ for all $x$ and $y$.
11158
Proof that a continuous function with $f(x) = f(x^2)$ is constant.
95469
Suppose $f:[0,1] \Rightarrow \mathbb{R}$ is continuous and $\int_0^x f(x)dx = \int_x^1 f(x)dx$. Prove that $f(x) = 0$ for all $x$
5416
How does one prove if a multivariate function is constant?
76148
Show that $\exists c \in \mathbb{R} : f(c) = 0$
72856
Show $f$ is constant if $|f(x)-f(y)|\leq (x-y)^2$.
84510
If $f(\mathbb{C})\subset \mathbb{C}-[0,1]$ then $f$ is constant
45342
Generalization of Mean Value Theorem to functions, $f: \mathbb{R}^n \rightarrow \mathbb{R}^n$
91947
Proof of $ f:I_n \rightarrow I_m \Rightarrow n = m$
115636
Show that $f$ is either injective or a constant function.
104044
Prove continuous functions $f$ and $g$ are equal
35378
Prove that $f$ analytic, $f(x) \in \mathbb{R}$ for all $x \in \mathbb{R}$ implies $f(\overline{z})=\overline{f(z)}$
97104
Proof that continuous function on $ [0, 2]$ has $f(x) = f(x-1)$ for some $ x$
102918
Prove $\sin x$ is uniformly continuous on $\mathbb R$
40209
$f : S^1 \to\mathbb R$ is continuous then $f(x)=f(-x)$ for some $x\in S^1$
64381
Prove that if one of $\lim_{x \rightarrow 0 }{f(x)}$ and $\lim_{x \rightarrow 0}{f(x^3)}$ exists, then the other one also exists.