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Directions: Questions No. 86 are Assertion - Reason type questions. Each of these questions contains two statements: Statement-1 (Assertion) and Statement-2 (Reason). Each of these questions also have four alternative choices, only one of which is the correct answer. You have to select the correct choice. Let \[f(x)={{(x+1)}^{2}}1,\text{ }x\ge 1\] Statement - 1: The set\[\{x:f(x)={{f}^{-1}}(x)\}\] \[=\{0,\text{ }1\}\]. Statement - 2: f is a bijection.     AIEEE  Solved  Paper-2009

A) Statement-1 is true, Statement-2 is true, Statement-2 is a correct explanation for statement-1

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

C) Statement-1 is true, statement-2 is false.

D) Statement-1 is false, Statement-2 is true

Correct Answer: A

Solution :

\[{{(x+1)}^{2}}1=x\] \[{{(x+1)}^{2}}=x+1\] \[\Rightarrow \] \[x=0,-1\] Since co-domain of function is not given. So if we assume function as onto then A is correct as not onto then none of the answer is correct.