document.write( "Question 1040392: Can I please have your assistance? 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: D arrow 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: P arrow F where lady (p) is the name of the first lady of the U.S. during the presidency of president p. Question: Which of the following functional inverses exist and which do not? pres -1, lady -1 (lady o pres) -1, (pres o lady) -1 \n" ); document.write( "

Algebra.Com's Answer #655321 by robertb(5830) $\"\"$ $\"About$

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(pres o lady)-1 or $\"%28pres%28lady%29%29%5E%28-1%29\"$ will not exist, because pres o lady is undefined.
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\n" ); document.write( "(lady o pres)-1 or $\"%28lady%28pres%29%29%5E%28-1%29\"$ exists, because any first lady can be matched to only one presidential inauguration date (of her president husband.)\r
\n" ); document.write( "\n" ); document.write( " $\"%28lady%29%5E%28-1%29\"$ exists, because any first lady can be matched to only one president (who is her husband). (No first lady was ever a wife to two
\n" ); document.write( "different presidents.)\r
\n" ); document.write( "\n" ); document.write( " $\"%28pres%29%5E%28-1%29\"$ exists, because any president can be matched to exactly one inauguration date. (No president has two inauguration dates, at
\n" ); document.write( "least in theory...)\r
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