Thank you for writing.
The image cannot be seen, as it is covered by the fill elements of the action button and the arrow button. Here is how to hide their fills, hence show the background image:
radSplitButton1.DropDownButtonElement.ActionButton.ButtonFillElement.Visibility = ElementVisibility.Collapsed;
radSplitButton1.DropDownButtonElement.ArrowButton.Fill.Visibility = ElementVisibility.Collapsed;
If this is not what you are trying to achieve, please let me know of the desired outcome and I will help you achieve it.
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