You can use any FX lens on a DX camera. You just get the cropped DX sensor area view on it which means you end up with a DX view of 24mm-52mm. Many people use FX lenses on DX bodies.....especially bird and sports folks with long tele lenses to get the maximum reach/coverage.
For the future, when putting an FX lens on a DX body, multiply the focal length by 1.5 for Nikon. (examples: 16mmx1.5=24mm.......300mmx1.5=450mm).
Using a DX lens on a FX body is another thread and not worth doing anyway.