The function f is defined by the equation f x = 100 x + 2 .

Choice D is correct. Substituting $9$ for $x$ in the given equation yields $f\left(9\right)=100\left(9\right)+2$, or $f\left(9\right)=902$. Therefore, the value of $f\left(x\right)$ when $x=9$ is $902$.

Choice A is incorrect. This is the value of $f\left(x\right)$ when $x=1.09$.

Choice B is incorrect. This is the value of $f\left(x\right)$ when $x=1.16$.

Choice C is incorrect. This is the value of $f\left(x\right)$ when $x=8.98$.