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DIRECTIONS : This question contains two statements: Statement-1 (Assertion) and Statement-2 (Reason). This question also has four alternative choices, only one of which is the correct answer. You have to select the correct choice. Let f(x)=(x+1)^2−1, x≥−1 Statement-1 : The set {x : f(x)=f^{-1}(x)}={0,−1}. Statement-2 : f is a bijection.

1. Statement-1 is true, Statement-2 is true. Statement-2 is not a correct explanation for Statement-1.
2. Statement-1 is true, Statement-2 is false.
3. Statement-1 is false, Statement-2 is true.
4. Statement-1 is true, Statement-2 is true. Statement-2 is not a correct explanation for Statement-1.

Correct answer: Statement-1 is false, Statement-2 is true.

Solution

Statement-1 is incorrect because the equation f(x) = f^{-1}(x) does not yield the set {0, -1}; rather, it has no solutions in the specified domain. Statement-2 is correct as the function f is indeed a bijection, being both one-to-one and onto within its domain.

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