Question

If $f\left(x\right)=x^n,n\in N$ and $\left(gof\right)\left(x\right)=ng\left(x\right)$ then $g\left(x\right)$ can be

• A. $n|x|$
• B. $3.\sqrt[3]{3x}$
• C. $e^x$
• D. $\log |x|$

Answer 1

Answer: (D)

$\log |x|$

$f\left(x\right)=x^n$

$g\left(f\right(x\left)\right)=ng\left(x\right)$ ...$\left(i\right)$

$\log \left(f\right(x\left)\right)=n\log \left(x\right)$ ...$\left(ii\right)$

Taking $\log \left(|x|\right)$ as $g\left(x\right)$ the above expression is reduced to eq $i$.

Hence

$g\left(x\right)=\log \left(|x|\right)$.