  We investigate the viability of f(R) theories in the framework of the
Palatini approach as solutions to the problem of the observed accelerated
expansion of the universe. Two physically motivated popular choices for f(R)
are considered: power law, f(R) = \beta R^n, and logarithmic, f(R) = \alpha
\ln{R}. Under the Palatini approach, both Lagrangians give rise to cosmological
models comprising only standard matter and undergoing a present phase of
accelerated expansion. We use the Hubble diagram of type Ia Supernovae and the
data on the gas mass fraction in relaxed galaxy clusters to see whether these
models are able to reproduce what is observed and to constrain their
parameters. It turns out that they are indeed able to fit the data with values
of the Hubble constant and of the matter density parameter in agreement with
some model independent estimates, but the today deceleration parameter is
higher than what is measured in the concordance LambdaCDM model.
