If f(x) = x² and g(x) = -2f(x+1) + 3, what is g(2)?

Rewrite $g$ using $f(x)=x^2$: $g(x)=-2f(x+1)+3=-2(x+1)^2+3$. At $x=2$: $-2(3)^2+3=-2(9)+3=-18+3=-15$, choice A. Choice C ($-3$) forgets to square $x+1$, giving $-2(3)+3$. Choice B ($-9$) treats $(x+1)^2$ as $2\cdot3=6$ instead of $3\cdot3=9$. Choice D ($21$) flips the sign on the coefficient, $2(9)+3$, which ignores the negative in $-2$. Always evaluate the inside of $f$ first, then apply $f$, and only then multiply and add. Writing the rewritten function first avoids sign mistakes with the negative coefficient.