# Let f be a function defined by () ( ) ( ) 2 fx x x =- + ³ 1 1, 1 . Statement – 1 : The set { () ()} { } 1 xfx f x : 1,2 . – = = Statement – 2 : f is a biection and ( ) 1 fx x x 1 1, 1.

Question:

Let $f$ be a function defined by

$f(x)=(x-1)^{2}+1,(x \geq 1)$

Statement – 1: The set $\left\{x: f(x)=f^{-1}(x)\right\}=\{1,2\}$.

Statement – 2 : $f$ is a bijection and

$$f^{-1}(x)=1+\sqrt{x-1}, x \geq 1 \text {. }$$

1. Statement- 1 is true, Statement- 2 is true; Statement- 2 is a correct explanation for Statement-1.

2. Statement- 1 is true, Statement- 2 is true; Statement- 2 is NOT a correct explanation for Statement-1.

3. Statement- 1 is true, Statement- 2 is false.

4. Statement-1 is false, Statement- 2 is true.

Correct Option: 1

JEE Main Previous Year 1 Question of JEE Main from Mathematics Sets, Relations and Functions chapter.
JEE Main Previous Year 2011 RS

Solution:

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