Find $f$ if $ f(x)+f\left(\frac{1}{1-x}\right)=x $
110704
Find all functions $f$ such that $f(x)+f(\frac{1}{1-x})=x$
54513
Prove $\frac 1{x+1}<\ln\left(\frac{x+1}x\right)<0.5\left(\frac 1x+\frac 1{x+1}\right)$
27809
Find the function equation $f(x+f(y)+yf(x))=y+f(x)+xf(y)$
1582
$f(x+1)-f(x)$ converges $\Rightarrow\frac{f(x)}x$ converges
69653
Inequality $\left(a-1+\frac{1}b\right)\left(b-1+\frac{1}c\right)\left(c-1+\frac{1}a\right)\leq1$
156778
Finding functions satisfying $f(f(x))+f(x)+x=0$
28286
About finding the function such that $f(xy)=f(x)f(y)-f(x+y)+1$
23217
About $\lim \left(1+\frac {x}{n}\right)^n$
88683
Functional equation $f\left(\frac{x+y}{2}\right)+f\left(\frac{2xy}{x+y}\right)=f(x)+f(y)$ implies $2f(\sqrt{xy})=f(x)+f(y)$
122407
If $f(x) = x^3+3x+4\;,$ Then value of $ \int_{-1}^{1}f(x)dx+\int_{0}^{4}f^{-1}(x)dx$
40487
Given $\lim_{x \rightarrow a}f(x)+\frac1{\left|f(x)\right|}=0$, what is $\lim_{x \rightarrow a}f(x)$?
98255
Find $f(x)$ such that $f(f(x)) = x^2 - 2$
2414
If $f \in \operatorname{Hol}(D)$, $f(\frac{1}{2}) + f(-\frac{1}{2}) = 0$, prove that $|f(0)| \leq \frac{1}{4}$
64339
Find $f$ where $f'(x) = f(1+x)$
6830
Find $\int\frac1x\sqrt\frac{1-x}{1+x}\ dx$
6482
Why aren't the functions $f(x) = \frac{x-1}{x-1}$ and $f(x) = 1$ the same?
61782
How to prove that $f(x) = \frac{-2x+1}{(2x-1)^2-1}$ is one-to-one on $(0,1)$?