Dear Colleagues,

Could you please help in solving the following problem:

Show that the norm $\displaystyle ||f||$ of a bounded linear functional $\displaystyle f\neq 0$ on a normed space $\displaystyle X$ can be interpreted geometrically as the reciprocal of the distance $\displaystyle d=inf\{||x|| \ |f(x)=1\}$ of the hyperplane

$\displaystyle H_{1}=\{x\in X \ |f(x)=1\}$ from the origin.

Regards,

Raed.