what is difference between co-domain and range?

Answer 1

That's one I just learned last semester, and I'm 34.

Most of the time, they are the same thing, but there's a very subtle difference.

Remembering that a function is a machine that takes an input and produces an output:

* The range is the set of all possible outputs you can get, if you tried every possible input element in the domain.
* The codomain can be larger than the range; it's just the set that the function maps to.

So the range is always a subset of the codomain.

The best example I know is:

You can say that:

f(x) = x²

Is a function that maps the set of real numbers to the set of real numbers. But, in reality, you can only get positive numbers out. So the codomain is all real numbers, and the range is all real numbers greater than or equal to zero.