An organ that receives both sympathetic and parasympathetic fibers is said to have what?

The answer is Dual Innervation.

Explanation:

The condition described in the question where an organ receives input from both the sympathetic and the parasympathetic fibers, which are two different parts of the nervous system in our body, is said to have a "Dual Innervation". Heart can be a perfect example for this case. This situation results in clashing signals at times, one system signaling the heart to pump faster and the other one signaling it to slow down.

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