  In this paper, we investigate a simple class of Horndeski models where the
scalar field plays the role of a k-essence fluid. We present several solutions
for early-time universe, namely inflation and cosmological bounce, by making
use of some reconstruction technique. Moreover, we furnish the formalism to
calculate perturbations in FRW space-time and we compute the spectral index and
the tensor-to-scalar ratio during inflation.
