Question

Assertion :$f\left(x\right)=\frac{1}{x-7}$ is decreasing $\forall xϵR-\left\{7\right\}$ Reason: $f^{\prime }\left(x\right)<0\forall x\ne 7$

• 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 A Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

$f\left(x\right)=\frac{1}{x-7}$
$\Rightarrow$ $f^{\prime }\left(x\right)=\frac{-1}{{(x-7)}^2}<0\forall xϵR-\left\{7\right\}$
Since $f^{\prime }\left(x\right)<0\forall x\ne 7\Rightarrow f\left(x\right)$ is decreasing
Hence Assertion is correct and reason is also correct and it is correct explanation of Assertion.