  A complete characterization of two functions $f(x,y)$ and $g(x,y)$ in the
$(f,g)$-inversion is presented. As an application to the theory of
hypergeometric series, a general bibasic summation formula determined by
$f(x,y)$ and $g(x,y)$ as well as four arbitrary sequences is obtained which
unifies Gasper and Rahman's, Chu's and Macdonald's bibasic summation formula.
Furthermore, an alternative proof of the $(f,g)$-inversion derived from the
$(f,g)$-summation formula is presented. A bilateral $(f,g)$-inversion
containing Schlosser's bilateral matrix inversion as a special case is also
obtained.
