Geoemtric interpretation of the norm of a bounded linear functional

Dear Colleagues,

Could you please help in solving the following problem:
Show that the norm of a bounded linear functional on a normed space can be interpreted geometrically as the reciprocal of the distance of the hyperplane
from the origin.

Regards,

Raed.

Quote:

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Originally Posted by raed

Dear Colleagues,

Could you please help in solving the following problem:
Show that the norm of a bounded linear functional on a normed space can be interpreted geometrically as the reciprocal of the distance of the hyperplane
from the origin.

Regards,

Raed.

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What have you tried? Where are you stuck? Please make an effort.