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Question:

Let f(x) = (x+1)² - 1, x ≥ -1. Statement-1: The set x: f(x) = f(-1) = 0, -1. Statement-2: f is a bijection. Statement 1 is true, Statement 2 is true, Statement 2 is a correct explanation for statement 1. Statement 1 is true, Statement 2 is true; Statement 2 is not a correct explanation for statement 1. Statement 1 is false, Statement 2 is true. Statement 1 is true, statement 2 is false.

Statement 1 is true, Statement 2 is true,Statement 2 is a correct explanation for statement 1

Statement 1 is true, Statement 2 is true; Statement 2 is not a correct explanation for statement 1.

Statement 1 is true, statement 2 is false.

Statement 1 is false, Statement 2 is true

Solution:

The co-domain of the given function is [-1, ∞). Now, Let y = (x+1)² - 1 ⇒ x = √y + 1 - 1 ∴ f⁻¹(x) = √y + 1 - 1, which exists ⇒ domain = co-domain. Therefore, the function f is one-one onto or bijection. Hence, option 'A' is correct.