Prove that $f(x)$ is a constant function.
58901
Why is every such function constant: $f(x)=f(x^2)$ for $x \in [0,1]$?
82001
How to prove the function is a constant
104044
Prove continuous functions $f$ and $g$ are equal
111458
Prove that $f$ is differentiable
61500
If f is continous and exist real numbers show that $f(x)=0$
91352
If $\Re(f)$ is bounded then f is constant.
3818
Proving two entire functions are constant.
154034
Suppose that $f(x)$ is continuous on $(0, \infty)$ such that for all $x > 0$,$f(x^2) = f(x)$. Prove that $f$ is a constant function.
30860
Prove that $f(x)=0$ in $[-1,1]$.
121771
Proof $f(x)\equiv 0$
97371
Proving a function is constant, under certain conditions?
14578
Proving that an additive function $f$ is continuous if it is continuous at a single point
34223
Prove that every function that verifies $|f(x)-f(y)|\leq(x-y)^2$ for all $x,y$ is constant.
34719
Show this holomorphic function is constant
74583
Prove that $f'(0)=L$.
105068
Proving that the function is differentiable and $f'(0)=0$
69008
$f'(x) = [f(x)]^{2}$. Prove $f(x) = 0 $