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help its answer is option (b)

help its answer is option (b)

Question Image
Grade:12

1 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
7 years ago
Ans:
Hello Student,
Please find answer to your question below

It is given that exactly one statement is true out of three.
Case I: Statement 1 is true
which means f(x) = 1 &
f(y) not equal to one is wrong. So f(y) have to be equal to 1.
So f take same value at both x & y which cant be possible b/c f is one-one function.
Case II: Statement 2 is true
f(y) not equal to 1 is true which means f(y) is either 2 or 3.
& f(x) = 1 is false which means f(x) will be either 2 or 3.
and f(z) not equal to 2 is false which means f(z) have to be 2.
So f will take output 3 at both x & y which cant be possible since f is one-one.
Cae III: Statement 3 is true
f(z) not equal to 2 is true which means f(z) will either be 1 or 3.
f(y) is false; f(y) have to be 1
f(x) = 1 is false which means f(x) will either be 1 or 3.
So this case seems good according to one-one condition.
So
f(y) = 1
f^{-1}(1) = y

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