dom variable $x,$ and $f(x)$ is a function of $x.$

$E[f]={\displaystyle \underset{x}{\overset{?}{}}}f(x)p(x)$

also consider the variance $({}^2$ or simply var$)$ for $f$ is expressed as:

var$[f]=E[f^2]-E[f{]}^2$

show the following equations are equivalent, if we consider using a constant value $()$ :

$E[f]=E[f]$

var$[f]={}^2$var$[f]$