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# If $f(x)=x^2\:\:and\:\:g(x)=2^x$ and $fog(x)=gof(x)$ then $x$ = ?

$\begin{array}{1 1} {0,2} \\ {0} \\{2} \\ none\;of\;these \end{array}$

$fog(x)=\big(2^x\big)^2=2^{2x}$
$gof(x)=2^{x^2}$
$2^{2x}=2^{x^2}\:\Rightarrow\:x^2=2x$
$\Rightarrow\:x=\{0,2\}$

+1 vote