Prove function is constant
113975
Let $f:\mathbb{R}\to\mathbb{R}$, $f(kx)=f(x)$. Show that if $f$ is continuous at $0$ then $f$ is a Constant function
115636
Show that $f$ is either injective or a constant function.
3818
Proving two entire functions are constant.
135129
Proving an entire  function which misses a ball is constant
105172
Prove that the entire function is constant over certain conditions.
142494
Functions $f(x)/g(x), g(x)/h(x),h(x)/f(x)$ are constant
100765
If $f'(x) = 0$ for all $x \in \mathbb{Q}$, is $f$ constant?
110112
Proving a function is Lipschitz continuous
104044
Prove continuous functions $f$ and $g$ are equal
77267
Given $f$ is continuous and $f(x)=f(e^{t}x)$ for all $x\in\mathbb{R}$ and $t\ge0$, show that $f$ is constant function
121771
Proof $f(x)\equiv 0$
126256
Prove limit of function
158888
Prove that the function $f(x)=\frac{x}{x^2+1}$ is continuous at $x=-1$.
53627
Proving continuity of $f$
727
Prove that any continuous integer-valued function of a real variable is constant.
145573
How to show that $f$ is a zero function?
114488
If $|f|+|g|$ is constant on $D,$ prove that holomorphic functions $f,~g$ are constant on $D$.