  We present a density-functional theory for the one dimensional harmonically
trapped Bose-Fermi mixture with repulsive contact interactions. The ground
state density distribution of each component is obtained by solving the
Kohn-Sham equations numerically based on the Local Density Approximation and
the exact solution for the homogeneous system given by Bethe ansatz method. It
is shown that for strong enough interaction, a considerable amount of fermions
are repelled out of the central region of the trap, exhibiting partial phase
separation of Bose and Fermi components. Oscillations emerge in the Bose
density curves reflecting the strong correlation with Fermions. For infinite
strong interaction, the ground state energy of the mixture and the total
density are consistent with the scenario that all atoms in the mixture are
fully fermionized.
