Question

Assertion :Let f(x) is a bijective function. Then
$f\left(x\right)=f^{-1}\left(x\right)\Rightarrow f^{-1}\left(x\right)=x$ Reason: $f^{-1}\left(x\right)=x\Rightarrow f\left(x\right)=f^{-1}\left(x\right)$.

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• C. Assertion is correct but Reason is incorrect
• D. Both Assertion and Reason are incorrect

Answer 1

The correct option is B Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion

Statement - I :

Let $f\left(x\right)=\frac{1}{x}\Rightarrow f^{-1}\left(x\right)=\frac{1}{x}$

$f\left(x\right)=f^{-1}\left(x\right)\Rightarrow xϵR_0\nRightarrow f\left(x\right)=x$

as $f\left(x\right)=x$ holds only on $x=\pm 1$.

$\Rightarrow$ statement- I is false

Statement - II
$f^{-1}\left(x\right)=x\Rightarrow f^{-1}\left(f\right(x\left)\right)=f\left(x\right)\Rightarrow x=f\left(x\right)$