  Several different explicit reconstructions of f(R) gravity are obtained from
the background FRW expansion history. It is shown that the only theory whose
Lagrangian is a simple function of the Ricci scalar R, that admits an exact
LCDM expansion history is standard General Relativity with a positive
cosmological constant and the only way to obtain this behaviour of the scale
factor for more general functions of R is to add additional degrees of freedom
to the matter sector.
