  In this paper we elaborate on the relation between the entropy formula of
Wald and the "entropy function" method proposed by A. Sen. For spherically
symmetric extremal black holes, it is shown that the expression of extremal
black hole entropy given by A. Sen can be derived from the general entropy
definition of Wald, without help of the treatment of rescaling the AdS_2 part
of near horizon geometry of extremal black holes. In our procedure, we only
require that the surface gravity approaches to zero, and it is easy to
understand the Legendre transformation of f, the integration of Lagrangian
density on the horizon, with respect to the electric charges. Since the Noether
charge form can be defined in an "off-shell" form, we define a corresponding
entropy function, with which one can discuss the attractor mechanism for
extremal black holes with scalar fields.
