Katy
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Mosaic To New Raster—Data Management toolbox | ArcGIS Desktop
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Mosaic—Data Management toolbox | ArcGIS Desktop
The mosaic allows you to combine 2 or more together... of course this means that you would experiment on copies of your originals to ensure you get it right.
Also, you should know the formats of the two and it is always best to make any changes before hand so you are in full control of the process. For instance, if they are different cell size, you should resample one, so that you have inputs with the appropriate cell size.
Of course, some of the things you should do manually (so you are in full control) are done quasi- automagically! You would know what was done during the process just to check.
The more you know about what you have, the better your results.
Don't take shortcuts or think that a tool that involves fewer steps is the best tool to use.
Experiment for yourself, just to be sure