Sure! Let's consider the function f(x) = x^2, which maps real numbers to non-negative real numbers.

* The co-domain of f is the set of all non-negative real numbers. We can denote it as CoD(f) = [0, ∞). This is the set of all possible outputs that f can produce.

* The image of f is the set of all non-negative real numbers that are actually produced by the function. In other words, it's the set of all values that f(x) takes on for some input x. We can denote it as Im(f) = {y | y = f(x) for some x}.

For example, if we consider the input set {1, 2, 3}, the outputs of f(x) for these inputs are {1, 4, 9}. So the image of f is {1, 4, 9}, and it's a subset of the co-domain [0, ∞).

So in this case, the co-domain is the set of all possible outputs (non-negative real numbers), and the image is the subset of non-negative real numbers that are actually produced by the function.
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