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begin quote ita"
CHAPTER I [:] Notions from Set Theory [...] 3. FUNCTIONS. "end quote
These pages assume that the reader has the book and is reading along.    
topic index     contents
Please read these notes from the beginning to here and then paragraph 9 of 3.

THE INVERSE IMAGE OF A SET UNDER A FUNCTION

begin quote ita-1-3-8-pg10 "
If   f : XY   is a function and   Y Y,   then the subset of   X   given by


f ( Y ) = { xX   :   f (x)Y }
[...]
is called the inverse image of   Y under   f.   It consists of those elements of   X   which correspond under   f   to elements of   Y .
"end quote

And now, without confusion (among those who have mastered the concepts I suppose):

begin quote ita-1-3-7-pg10 "
If   f : XY   happens to be one-one onto we have another use for the symbol   f ,   namely the inverse function   f : YX.   These two uses of   f   must be carefully distinguished, though confusion rarely arises.   If   f : XY   is one-one onto then the two uses of   f are related by

{ f (y) } = f ( { y } )   for each   yY.
"end quote

To avoid confusion, just look again at the topic of this page. If what is inside the parentheses is a set, then we have the inverse image of a set.

on to 4 ?