In the paper we will examine when the inverses of one-to-one
Sierpinski-Zygmund partial functions from **R** to **R** are
also
of Sierpinski-Zygmund type. We show that the existence of
a partial Sierpinski-Zygmund function f with f^{-1} being also
Sierpinski-Zygmund is independent of ZFC
axioms of set theory. However, there exists
a one-to-one Sierpinski-Zygmund injection f:**R**-->**R**
such that f^{-1} is not Sierpinski-Zygmund.
This work is related to the investigation of
algebraic properties of the Sierpinski-Zygmund functions
discussed in
K. Ciesielski, T. Natkaniec,
Algebraic properties of the class of Sierpinski-Zygmund functions.

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**Last modified January 11, 1999.**