Question 329096
You're correct up to expanding the function,
{{{2{x-3}^2+1=4x^2-24x+37}}} 
The leading coefficient should be a 2 and not a 4. 
You seem to have doubled up somehow.
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{{{f(x)=2x^2+1 }}}
{{{g(x)=x-3}}}
{{{f(g)=2g^2+1}}}
{{{f(g)=2(x-3)^2+1}}}
{{{f(g)=2(x^2-6x+9)+1}}}
{{{f(g)=2x^2-12x+18+1}}}
{{{f(g)=2x^2-12x+19}}}