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)}
(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 , b u t F ( b ) = F ( c ) = 1 . So, it is not one-one. F is not invertible.
Therefore, the function F − 1 doesn’t exists.
(i)
Given function
A function is said to be an inverse function if it is both one-one and onto.
As
Thus, the function
(ii)
Given, function
A function is said to be an inverse function if it is both one-one and onto.
As
Therefore, the function
