Composite function ...

Question

Given the two functions:

$$f: x \in \mathbb{Z} \to 4 - x \in \mathbb{Z}$$

$$g: y \in \mathbb{Z} \to |y| + 3 \in \mathbb{N}$$

The composite function is:

$$g \circ f: |4 - x| + 3$$

Please tell me if it's correct, thanks.

Answer 1

The mapping of the composite function $g \circ f$ is correct, but in order to fully specify the function it is crucial to also state domain and codomain of the function.

Using the notation above we can write \begin{align*} g \circ f: x \in \mathbb{Z} \to |4 - x| + 3 \in \mathbb{N} \end{align*}

Hint: For instance in order to determine surjectivity of a function we also have to consider domain and codomain.