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Determining the im(f) watch

1. Just want to check my understanding of determining the image of a function. Am I correct in saying that to do this we need to show that the im(f) is a subset of the co-domain, and that an element of the domain maps to the im(f)?

I tried an example that has a worked solution and from that it looks like that's what has happened.
2. (Original post by Music99)
Just want to check my understanding of determining the image of a function. Am I correct in saying that to do this we need to show that the im(f) is a subset of the co-domain, and that an element of the domain maps to the im(f)?

I tried an example that has a worked solution and from that it looks like that's what has happened.
Yes, the image of the domain under f, will be a subset of the codomain, and for each element in the image of f, there must be an element in the domain that maps to it, by definition of the image of f.
3. (Original post by Music99)
Just want to check my understanding of determining the image of a function. Am I correct in saying that to do this we need to show that the im(f) is a subset of the co-domain, and that an element of the domain maps to the im(f)?

I tried an example that has a worked solution and from that it looks like that's what has happened.
You don't need to show that it is a subset of the codomain since by the definition of a function, the image is in the codomain.

The image of a function is the set

so you could use either of those two equivalent formulations - either consider each element of the codomain and determine whether it is of the form f(x) for some x in the domain or else you could consider the form of f(x) for each element x in the domain. There isn't a great deal of difference and it also depends how you are given the function.

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Updated: May 14, 2013
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