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Recall that if R is a relation, then we can look at the inverse relation R^ -1 ={ (y,x):(x,y) in R} . Show that for a function F: X -> Y, F ^ - 1 is a (total) function if and only if F is bijective.

Recall that if R is a relation, then we can look at the inverse relation R^ -1 ={ (y,x):(x,y) in R} . Show that for a function F: X -> Y, F ^ - 1 is a (total) function if and only if F is bijective.

College Algebra
College Algebra
1st Edition
ISBN:9781938168383
Author:Jay Abramson
Publisher:Jay Abramson
Chapter3: Functions
Section3.3: Rates Of Change And Behavior Of Graphs
Problem 2SE: If a functionfis increasing on (a,b) and decreasing on (b,c) , then what can be said about the local...
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2. Recall that if R is a relation, then we can look at the inverse relation R^ -1 ={ (y,x):(x,y) in R} . Show that for a function F: X -> Y, F ^ - 1 is a (total) function if and only if F is bijective.
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