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If A = {a, b, c, d} and f = {a, b), (b, d), (c, a), (d, c)}, show that f is one-one from A onto A. Find f–1

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Question

If A = {a, b, c, d} and f = {a, b), (b, d), (c, a), (d, c)}, show that f is one-one from A onto A. Find f–1

Sum
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Solution

f is one-one since each element of A is assigned to distinct element of the set A.

Also, f is onto since f(A) = A.

Moreover, f–1 = {(b, a), (d, b), (a, c), (c, d)}

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Chapter 1: Relations And Functions - Solved Examples [Page 4]

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NCERT Exemplar Mathematics Exemplar [English] Class 12
Chapter 1 Relations And Functions
Solved Examples | Q 10 | Page 4

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