Answer
The light is four times as bright.
Work Step by Step
By moving halfway to the lamp, $x$ is divided by $2$. Thus, by the inverse square law:
$f(x) = k(\frac{x}{2})^{-2}$
$f(x) = \frac{k}{\frac{x^2}{2^2}}$
$f(x) = \frac{k}{\frac{x^2}{4}}$
$f(x) = \frac{4k}{x^2}$
Which means there is 4 times as much illumination, or the light is four times as bright.
