Nonlinear functions SAT question

Choice B is correct. It’s given that $f(x)=9{(4)}^x$ and $g(x)=f(x+2)$. Substituting $x+2$ for $x$ in $f(x)=9{(4)}^x$ gives $f(x+2)=9{(4)}^{x+2}$. Rewriting this equation using properties of exponents gives $f(x+2)=9{(4)}^x{(4)}^2$, which is equivalent to $f(x+2)=9{(4)}^x(16)$. Multiplying $9$ and $16$ in this equation gives $f(x+2)=144{(4)}^x$. Since $g(x)=f(x+2)$, $g(x)=144{(4)}^x$.

Choice A is incorrect and may result from conceptual or calculation errors.

Choice C is incorrect and may result from conceptual or calculation errors.

Choice D is incorrect and may result from conceptual or calculation errors.