No, the inverse of a function is not always a function. For the inverse of a function to be a function itself, the original function must be bijective, meaning that it is both injective (one-to-one) and surjective (onto). If a function is not bijective, then its inverse will not be a function because it will fail the vertical line test, which states that a vertical line should only intersect a function at most once for it to be considered a function.
