Question

Assertion :$f:R\to R$ is a function defined by $f\left(x\right)=\frac{5x-8}{3}$ then $f^{-1}\left(x\right)=\frac{3x+8}{5}$ Reason: $f\left(x\right)$ is not a bijection.

• 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 C Assertion is correct but Reason is incorrect

Let $y=\frac{5x-8}{3}=f\left(x\right)$

$\Rightarrow 3y=5x-8$

$\Rightarrow x=\frac{3y+8}{5}\Rightarrow f^{-1}\left(y\right)=\frac{3y+8}{5}$

$\Rightarrow f^{-1}\left(x\right)=\frac{3x+8}{5}$

$\Rightarrow$ Assertion (A) is true but Reason (R) is false.