Can someone please explain to me in layman what each means? Perhaps with some examples with functions (inputs to outputs/numeric values in them)? Especially range, image, and preimage. So far this is my understanding:
- Domain is basically the input $x$ in $f(x)$.
- Codomain is what $f(x)$ produces as an output such as $y$ when $f(x) = y$.
- Range sounds like codomain but with some restriction?
- Image I have little understanding of but I think it is basically a relation between domain to codomain given that we take a subset of our function (Eg; it is the input to output process of our function given we put a restriction on the domain as $x$ can only go from $0$ to $1$).
- Preimage is just walking backward on the "image" process? (Inverse image?) Going from our "subsetted" output back to our "subsetted" input?
I am very frustrated that I can't seem to grasp these basic concepts so I would greatly appreciate any help from anyone who can break this down for me and help me understand it without too much mathematical notation. Thank you!