In researching the Nikon website I located the information pasted below. The answer is clearly "yes" the DX lense will function on an FX camera. If I interpret the information below correctly, using a DX lens on an FX camera will result in a cropping effect on the subject because the FX camera will default to its built-in DX crop mode. Net effect is you will not obtain the wide view perhaps desired e.g. a 24mm lens will provide an approximate 36mm view (example cited by NIKON).

PER NIKON:
In digital cameras, the camera's format refers to the size of its image sensor. Nikon makes a DX-format sensor and an FX-format sensor. The DX-format is the smaller sensor at 24x16mm; the larger FX-format sensor measures 36x24mm which is approximately the same size as 35mm film.

Different NIKKOR lenses are designed to accommodate the different camera sensor sizes. In the case of DX cameras with their smaller sensors, corresponding DX lenses have been designed. The DX designation can be found in the lens name, i.e. AF-S DX Zoom-NIKKOR 12-24mm f/4G IF-ED. These lenses are smaller and lighter in weight and address the market's need for affordable, high-performance lenses with a variety of focal lengths and zoom options.

The DX sensor makes possible the production of lighter, smaller cameras, but because it covers a smaller portion of the image projected by the lens, a 1.5x crop factor (so called because the smaller sensor crops the image compared to an image from a 35mm film frame) is introduced. This means, for example, a 24mm lens on a DX sensor camera will provide an approximate 36mm view.

The FX sensor, with more "light gathering" area, offers higher sensitivity and, generally, lower noise. There is, of course, no crop factor present with the FX sensor.

DX cameras have the added benefit of being able to use both DX and non-DX NIKKOR lenses-those lenses without the DX designation in their names, i.e. AF-S NIKKOR 14-24mm f/2.8G ED. And here's why.