  In this paper, we explore the equivalence between two theories, namely f(R)
and scalar-tensor theories of gravity. We use this equivalence to explore
several f(R) toy models focusing on the inflation epoch of the early universe.
The study is done based on the definition of the scalar field in terms of the
first derivative of f(R) model. We have applied the slow-roll approximations
during inflationary parameters consideration. The comparison of the numerically
computed inflationary parameters with the observations is done. We have
inspected that some of the f(R) models produce numerical values of $n_{s}$ that
are in the same range as the suggested values from observations. But for the
case of the tensor-to-scalar ratio $r$, we realized that some of the considered
f(R) models suffer to produce a value which is in agreement with the observed
values for different considered space parameter.
