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hi everyone in this video were going to talk about a special set thats associated with functions so say we have a function f from A to B a here is the domain and B is the codomain so were going to let W be a subset of the codomain so W is a subset of B and were going to define the following set so f inverse so like this of W this is the inverse image of W under F so inverse image of W under F its also called the pre image and this is probably one of the hardest if not the hardest set to work with when you first start dealing with functions so its the set of all elements in a so little a and a such that F of a is in W so said another way its the set of all elements in a that gets sent to W again its the set of all elements in a that gets sent to W let me draw a picture so you see what is going on so here is a and here is B and then W is going to be this purple set over here heres our W so the inverse image is a subset of a right because look its all of the little As in capit