f x = 9 ( 4 ) x The function f is defined by the given

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

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.