A compact microfocus x-ray source based on a high repetition rate, ultrafast laser-triggered field emission cathode is characterized. Bremsstrahlung and Cu Kα x-ray pulses are generated in a transmission geometry from 20-keV electrons incident on a thin Cu target. Timing correlations between optical and x-ray pulses show that the precision timing properties of the optical pulse train are transferred to the x-ray pulse train. Simple electron optics allow a demonstration of point-projection x-ray imaging. Modelling of the electron trajectories shows that sub-µm spot sizes and sub-100-fs x-ray pulse durations are feasible with improved electron optics.