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If $f(x)=x^n$, $n\in N$ and $gof(x)=ng(x)$, then $g(x)$ = ?

$\begin{array}{1 1} n|x| \\ 3x^{1/3} \\ e^x \\ log x \end{array}$

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Toolbox:
  • $logx^n=nlogx$
Given $f(x)=x^n$
$gof(x)=g(x^n)=ng(x)$
We know that $logx^n=nlogx$
$\therefore\:g(x)=logx$
answered May 27, 2013 by rvidyagovindarajan_1
 

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