Question

Assertion :$f$ is even, $g$ is odd then $\frac{f}{g}(g\ne 0)$ is an odd function. Reason: If $f(-x)=-f\left(x\right)$ for every $x$ of its domain then $f\left(x\right)$ is called odd function and if $f(-x)=f\left(x\right)$ for every $x$ of its domain, then $f\left(x\right)$ is called even function.

• 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

Let $h\left(x\right)=\frac{f\left(x\right)}{g\left(x\right)},(g\left(x\right)\ne 0)$

$\Rightarrow h(-x)=\frac{f(-x)}{g-\left(x\right)}=\frac{f\left(x\right)}{-g\left(x\right)}=-h\left(x\right)$

Assertion (A) & Reason (R) both are independently true & Reason (R) is the correct explanation of Assertion (A).