sat-dog

Choice D is correct. It's given that $f\left(x\right)=\frac{1}{6x}$. Substituting $3$ for $x$ in this equation yields $f\left(3\right)=\frac{1}{6\left(3\right)}$, or $f\left(3\right)=\frac{1}{18}$. Therefore, when $x=3$, the value of $f\left(x\right)$ is $\frac{1}{18}$.

Choice A is incorrect. This is the value of $f\left(x\right)$ when $x=0.5$.

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

Choice C is incorrect. This is the value of $f\left(x\right)$ when $x=1.5$.