Question

$A=$ the domain of $f$ where $f\left(x\right)=\log x^2$ and $B=$ the domain of $g$ where $g\left(x\right)=2\log x$, then $A-B=$

• A. $\varphi$
• B. $(-\infty ,0)$
• C. $(0,\infty )$
• D. $(0,1)$

Answer 1

Answer: (B)

$(-\infty ,0)$

$\log x$ is defined only for $x>0$

$\log x^2$ is defined for all $x\in (-\infty ,\infty )-\left\{0\right\}$

$\Rightarrow B=(0,\infty );A=(-\infty ,0)\cup (0,\infty )$

$\therefore A-B$ is $(-\infty ,0)$