Question

Assertion :If $f\left(x\right)=\log x^2$ and $g\left(x\right)=2\log x$ then $f\left(x\right)\ne g\left(x\right)$. Reason: $f\left(x\right)$ is defined $\forall x\in R-\left\{0\right\}$ and $g\left(x\right)$ is defined only for positive value of $x$ , so their domain are not equal (identical)

• 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

$=f\left(x\right)=\log x^2=2\log \left|x\right|\ne 2\log x$

$\Rightarrow f\left(x\right)\ne g\left(x\right)\therefore$ Assertion is true.

Again, $D_f=R-\left\{0\right\},D_g=(0,\infty )$

$\Rightarrow D_f\ne D_R$

$\Rightarrow$ Reason (R) is correct with correct explanation