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

Work from the inside out. First evaluate the inner function: $g(2)=2^2+1=5$. Then feed that result into $f$: $f(5)=2(5)-3=7$, choice D. Choice A reverses the order of composition: $f(2)=1$ and then $g(1)=2$, which is $g(f(2))$ and not $f(g(2))$. Choice C drops the $+1$ in $g$, using $g(2)=4$ and then $f(4)=5$. Choice B uses $f(x)=2x+3$ instead of $2x-3$, giving $f(5)=13$. The notation $f(g(2))$ always means apply $g$ first, then $f$ to that result.