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Question

If X and Y are two non-empty sets, where f:XYis function is defined such that f(C)=f(x):xC for CX and f-1(D)=x:f(x)Dfor DY, for any AY and BY, then


A

f-1fA=A

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B

f-1fA=A only if fX=Y

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C

ff-1B=B, only if BX

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D

ff-1B=B

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Solution

The correct option is C

ff-1B=B, only if BX


Explanation for the correct answer:

It is given that f:XY

f-1:YX

It is also given that AY and BY

Hence, only f-1A and f-1B are defined.

fA and fB cannot be defined as AYand BY

Nowf-1A and f-1B will give a value each in the set X

Hence, ff-1(A)=A and ff-1(B)=B are defined only if A,Bfx.

Hence, option (C) is the correct answer


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