Question

Assertion :If $g\left(x\right)$ is a differentiable function $g\left(1\right)\ne 0$, $g(-1)\ne 0$ and Rolle's theorem is not applicable to $f\left(x\right)=\frac{x^2-1}{g\left(x\right)}$ in $[-1,1]$, then $g\left(x\right)$ has at least one root in $(-1,1)$. Reason: If $f\left(a\right)=f\left(b\right)$, then Rolle's theorem is applicable for $xϵ(a,b)$.

• 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

for assertion-
All condition satisfies to function for roll's theorem.
for reason-
Function is not given differentiable and continous.