  In this work we show that the gravity lagrangian f(R) at relatively low
curvatures in both metric and Palatini formalisms is a bounded function that
can only depart from the linearity within the limits defined by well known
functions. We obtain those functions by analysing a set of inequalities that
any f(R) theory must satisfy in order to be compatible with laboratory and
solar system observational constraints. This result implies that the recently
suggested f(R) gravity theories with nonlinear terms that dominate at low
curvatures are incompatible with observations and, therefore, cannot represent
a valid mechanism to justify the cosmic speed-up.
