Let f be a function defined by

Question:

Let $\mathrm{f}$ be a function defined by $\mathrm{f}(\mathrm{x})=(\mathrm{x}-1)^{2}+1,(\mathrm{x} \geq 1)$

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

Statement - 2 : $f$ is bijection and $\mathrm{f}^{-1}(\mathrm{x})=1+\sqrt{\mathrm{x}-1}, \mathrm{x} \geq 1$

  1. Statement–1 is true, Statement–2 is false. 

  2. Statement–1 is false, Statement–2 is true. 

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

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


Correct Option: , 3

Solution:

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