Value of $f(2016),$ If $f(x) = f(2x)\forall x \in \mathbb{R}$ are given
132113
Does $f(x) = f(2x)$ for all real $x$, imply that $f(x)$ is a constant function?
55175
Is the function $f(x) = x^2 - 2x$ one-to-one?
155806
(Olympiad Question) $f(2x) + 2f(y) = f(f(x+y))$
95970
Let $f:[0,1] \rightarrow \mathbb{R}$ be a continuous function. If $f(0)=f(1)$ then exists $x\in [0,1]$ s.t. $f(x) = f(x+\frac{1}{2})$
150502
If $f(0) = 0$ and $|f'(x)|\leq |f(x)|$ for all $x\in\mathbb{R}$ then $f\equiv 0$
117353
Polynomial equation $f(x)f(2x^2)=f(2x^3+x)$
41226
Find $f:f(xf(x)+f(y))=f(x)^2+y$
3387
Derivative of $f(x)=|x|$
124629
If $f(x) = \frac{4^x}{4^x+2},$ find the value of $\sum \limits_{i=1}^{1999} f\left(\frac{i}{1999}\right) $
18905
$f(a)=f(b)=f_{+}'(a)=f_{-}'(b)=0$ and $|f''(x)|\le M$. Show that $|f(x)|\le \frac{M(b-a)^2}{16}$.
99458
Suppose $\int_{[a,b]}f=0,\text{ then }f(x)=0 \forall x\in[a,b]$
106013
Given $f(x) = x + |x|$ for what values of $x$ is $f$ differentiable
47135
Prove if a = b, then f(a) = f(b) for any function f (with natural deduction)
13248
How to obtain $f(x)$, if it is known that $f(f(x))=x^2+x$?
34077
Let $f:\mathbb{R}\to\mathbb{R}$ satisfy $f\big(x-f(y)\big)=f\big(f(y)\big)+x\cdot f(y)+f(x)-1$ for all $x,y\in\mathbb{R}$.
76458
Solve the following functional equation $f(xf(y))+f(yf(x))=2xy$
86367
Computing $f(x)$ if $\int_1^{xy} f(t) dt = y \int_1^x f(t) dt + x\int_1^y f(t) dt$ and $f(1) = 3$