The function f is defined by f x = 16 x . What is the value

Choice A is correct. It's given that $f\left(x\right)=\frac{16}{x}$. Substituting $17$ for $x$ in this function yields $f\left(17\right)=\frac{16}{17}$. Therefore, when $x=17$, the value of $f\left(x\right)$ is $\frac{16}{17}$.

Choice B is incorrect. This is the value of the reciprocal of $f\left(x\right)$ when $x=17$.

Choice C is incorrect. This is the value of $f\left(x\right)$ when $x=1$.

Choice D is incorrect. This is the value of $x$ when $x=17$.