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.

Correct answer: (C) Statement-1 is true, Statement-2 is false. There is no information about co-domain therefore f(x) is not necessarily onto.

Q56 / 90 · JEE Main 2009 · Mathematics

Let $f(x)=(x+1)^2-1, x \geq-1$ Statement-1: The set $\left\{x: f(x)=f^{-1}(x)\right\}=\{0,-1\}$ Statement-2 : $\mathrm{f}$ is a bijection.

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
Correct answer
C
Statement-1 is true, Statement-2 is false
D
Statement-1 is false, Statement-2 is true

There is no information about co-domain therefore $f(x)$ is not necessarily onto.

Hence, the correct answer is option: 'C'.