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Usually very little.

f(x) simply denotes the function f except that with this notation it is explicit that f(x) is a function of the variable x (and only x).

So, f = x + 3 and f(x) = x + 3 are equivalent.

However, there will be times, with functions of more than one variables where you wish to consider only one of the arguments while holding the other argument constant.

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Q: What is the difference in meaning between f and f x?
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