If I have the following function
$f(x)=1-x^c$ with $x$ being periodic and can be written in the form of $x(t)=Asin(wt)+B$. $c$ is real (most of the time not an integer) and $B$ is chosen in a way where $x(t)>0$
Then one can deduce directly that $f(\overline{x}) = \overline{f(x)}$ always if $B=0$ ($\overline{x}$ represents the mean value of x over one period).
Question How can I calculate analytically the difference $f(\overline{x}) - \overline{f(x)}$ when $B\neq 0$ ?