  In this paper, we analyzed inflation from k-essence in the framework of
Horndeski gravity. In the specific, we considered models of canonical scalar
field and k-essence with quadratic kinetic term. Viable inflationary models can
be reconstructed by starting from the cosmological data. Several possibilities
are explored in order to correctly reproduce the spectral index and the
tensor-to-scalar ratio of primordial cosmological perturbations.
