Let S = { a , b , c } and T = {1, 2, 3}. Find F −1 of the following functions F from S to T , if it exists. (i) F = {( a , 3), ( b , 2), ( c , 1)} (ii) F = {( a , 2), ( b , 1), ( c , 1)}

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Solution

(i)

Given function F:S→T is defined as F={ ( a,3 ),( b,2 ),( c,1 ) }.

A function is said to be an inverse function if it is both one-one and onto.

As F( a )=3, F( b )=2 and F( c )=1. So, it is one-one and onto.

Thus, the function F −1 exists and it is given by F −1 :T→S as,

F −1 ={ ( 3,a ),( 2,b ),( 1,c ) }.

(ii)

Given, function F:S→T is defined as F={ ( a,2 ),( b,1 ),( c,1 ) } .

A function is said to be an inverse function if it is both one-one and onto.

As F( a )=2, butF( b )=F( c )=1. So, it is not one-one. Fis not invertible.

Therefore, the function F −1 doesn’t exists.

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