Let*D
*be the set of all calendar dates from 4/30/1789 to 9/25/2014.
Let*P
*be the set of names of U.S. presidents.
Let*F
*be the set of names of first ladies of the U.S.
Consider the following two functions*pres
\rightarrow P
*where*pres(d)
*is the name of the president of the U.S. on date*d
*(the incumbent on inauguration days, to avoid ambiguity) and*lady \rightarrow F
*where*lady(p)
*is the name of the first lady of the U.S. during the presidency of president*p
.
1. Can the composition*pres \circ lady
*be defined? What about*lady \circ pres
?
2. Which of the following functional inverses exist and which do not?
***pres^{-1}
,*lady^{-1}
,*(lady \circ pres)^{-1}
,*
***(pres \circ lady)^{-1}
*be the set of all calendar dates from 4/30/1789 to 9/25/2014.
Let*P
*be the set of names of U.S. presidents.
Let*F
*be the set of names of first ladies of the U.S.
Consider the following two functions*pres
\rightarrow P*where*pres(d)
*is the name of the president of the U.S. on date*d
*(the incumbent on inauguration days, to avoid ambiguity) and*lady
\rightarrow F*where*lady(p)
*is the name of the first lady of the U.S. during the presidency of president*p
.
1. Can the composition*pres \circ lady
*be defined? What about*lady \circ pres
?
2. Which of the following functional inverses exist and which do not?
***pres^{-1}
,*lady^{-1}
,*(lady \circ pres)^{-1}
,*
***(pres \circ lady)^{-1}