prove that f is constant if $f(2^x)=f(3^x)$
50103
Show that a continuous function satisfying $f(2^x)=f(3^x)$ for $x\in (0,\infty)$ is a constant function
91352
If $\Re(f)$ is bounded then f is constant.
96450
If $f(x)$ is continuous and differentiable function , prove that $f(x) \geq e^{3x}, \forall x \geq 0$
67527
Proof by Induction that $3^n ≥ 1+2^n$
121771
Proof $f(x)\equiv 0$
97643
Prove that:$f(f(x)) = x^2 \implies \int_{0}^{1}{(f(x))^2dx} \geq \frac{3}{13}$
145919
If $f: \Bbb{R}\rightarrow\Bbb{R}$ is continuous at $0$ and $f(x)=f(2x)$ for each $x\in\Bbb{R}$ then $f$ is constant.
19355
prove $f(x)=x^3+x$ is one to one and onto
142138
Show that $f(x)$ is a constant function if $\lim\limits_{h\to 0}\frac{1}{h^3}\int_{-h}^{h}f(x+t)\cdot t\,dt=0$ for all $x$
27772
Let $f$ be an analytic function such that $\operatorname{Im}(f(z))=\operatorname{Re}(f(z))^2$. Prove that $f$ is constant.
100765
If $f'(x) = 0$ for all $x \in \mathbb{Q}$, is $f$ constant?
139744
For a continuous function $f$ show $\exists c\in (0,1)$ s.t $f(c)=3c^2$
59063
$f(f(x))=f(x)$ question
97184
Show: $ f(a) = a,\ f(b) = b \implies \int_a^b \left[ f(x) + f^{-1}(x) \right] \, \mathrm{d}x = b^2 - a^2 $
56127
Prove a function is constant under certain conditions
152617
Differentiate $f(x)=x^TAx$
64650
If $a\operatorname{Re}(f(z))+b\operatorname{Im}(f(z))=c$ then f is constant