Question

Which of the following functions are not identical?

• A. $f\left(x\right)=\ln x^2\text{and}g\left(x\right)=2\ln x$
• B. $f\left(x\right)={\log }_{x}e\text{and}g\left(x\right)=\frac{1}{{\log }_{e}x}$
• C. $f\left(x\right)=\sin \left({\cos }^{-1}x\right)\text{and}g\left(x\right)=\cos \left({\sin }^{-1}x\right)$, x$\in (0,1)$
• D. None of these

Answer 1

The correct option is A $f\left(x\right)=\ln x^2\text{and}g\left(x\right)=2\ln x$

Only Option one is not identical since
$f\left(x\right)=\log x^2$ has a domain $(-\infty ,0)\bigcup (0,\infty )$ while $f\left(x\right)=2\log x$ has a domain $(0,\infty )$