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Let the function f be given by f(x)=(x-1)^2+1 for x\ge 1. Statement-1: The solution set of f(x)=f^{-1}(x) is {1,2}. Statement-2: The function f is one-to-one and onto, and its inverse is f^{-1}(x)=1+\sqrt{x-1}, with x\ge 1.

1. Statement-1 is correct, Statement-2 is correct; Statement-2 correctly explains Statement-1.
2. Statement-1 is correct, Statement-2 is correct; Statement-2 does not correctly explain Statement-1.
3. Statement-1 is correct, Statement-2 is incorrect.
4. Statement-1 is incorrect, Statement-2 is correct.

Correct answer: Statement-1 is incorrect, Statement-2 is correct.

Solution

Statement-1 is incorrect because the solution set of f(x)=f^{-1}(x) does not yield only the values {1,2}, while Statement-2 is correct as it accurately describes the function f as one-to-one and onto, and provides the correct form of its inverse.

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