Choice A is correct. It's given that $g(x) = x^2 + 9$ . Substituting $25$ for $g(x)$ in this equation yields $25 = x^2 + 9$. Subtracting $9$ from both sides of this equation yields $16 = x^2$. Taking the square root of each side of this equation yields $x = ± 4$. It follows that $g(x) = 25$ when the value of $x$ is $4$ or $-4$. Only $4$ is listed among the choices.

Choice B 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.