Question

For any constant a, let

Answer 1

$g(x)=ax-2x\ln(x)\\\\x-intercept\ if\ g(x)=0\\\\subtitute\\\\ax-2x\ln(x)=0\\\\x=x(a-2\ln(x))=0\iff x=0\ or\ a-2\ln(x)=0\\\\Answer:\boxed{x=0}$

Answer 2

x-intercept => g(x) = 0
ax-2xln(x) = 0
x(a-2ln(x))=0

1. x=0 "F" because x>0

2. a-2ln(x)=0
ln(x)=a/2
$x= e^{ \frac{a}{2} }$