document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1121070>Question 1121070</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Let A = {1,2,3,4} and B = {a,b,c,d} and let f = {(1,a),(2,a),(3,d),(4,c)}. Show that f is a function but f^-1 is not a funtion </SPAN>\n" );
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document.write( "A relation is NOT a function if there are two (or more) different outputs for the same input.<br><BR>\n" );
document.write( "The given function is f: {(1,a),(2,a),(3,d),(4,c)}.  The inputs are all different, so there is no possibility that there are different outputs for the same input.<br><BR>\n" );
document.write( "Therefore f is a function.<br><BR>\n" );
document.write( "The inverse function is f^-1: {(a,1),(a,2),(d,3),(c,4)}.  Input a has two different outputs (1 and 2); therefore f^-1 is not a function. </SPAN>\n" );
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