  The properties of a classical simple liquid can be strongly affected by
application of an external potential that supports inhomogeneity. To understand
the nature of these property changes the equilibrium particle distribution
functions of the liquid have, typically, been evaluated individually as
functions of system control parameters, such as the packing fraction of a hard
sphere liquid. In this study we focus attention on two distribution functions
that characterize the inhomogeneous liquid: the pair direct correlation
function $c(\mathbf{r}_1,\mathbf{r}_2)$ and the pair correlation function
$g(\mathbf{r}_1,\mathbf{r}_2)$. We solve the Ornstein-Zernike equation for the
inhomogeneous liquid to obtain $c(\mathbf{r}_1,\mathbf{r}_2)$ as an explicit
function of $g(\mathbf{r}_1,\mathbf{r}_2)$, with the latter considered to be an
experimental observable, using information about the well studied and resolved
$g^0(\mathbf{r}_1-\mathbf{r}_2)$ and $c^0(\mathbf{r}_1-\mathbf{r}_2)$ for the
parent homogeneous ($^0$) system. The result obtained with our formulation is
tested against the exact solutions for the correlation and distribution
functions of a one-dimensional inhomogeneous hard rod liquid. Following the
success of that test the formalism is extended to obtain
$c(\mathbf{r}_1,\mathbf{r}_2)$ as an explicit function of
$g(\mathbf{r}_1,\mathbf{r}_2)$ in a three dimensional liquid.
