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thanks for help..........i have another question …....

thanks for help..........i have another question …....

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Grade:12

1 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
9 years ago
Ans:
Hello Student,
Please find answer to the following question

f(x, y ,z)\rightarrow (1, 2, 3)
is a one-one function.
So which means that every input has only one output.
Given:
f(x) = 1
f(y) \neq 1
f(z) \neq 2
Since only one statement is correct and function is one-one.
Function has output 1 at x.
So at y & z, it will have either 2 or 3.
f(z) can be either 2 or 3.
Since its not 2, so it will definitely be 3.
And f(y) be equal to 2.
So we have
f(x) = 1
f^{-1}(f(x)) = f^{-1}(1)
Since function is one-one and also onto.
So it can be invertible. So,
f^{-1}(f(x)) =x
f^{-1}(1) =x
Option (a) is correct.

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