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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.

idok
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Jon D
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    Looks good to me. – Arthur Jan 14 '18 at 17:24
  • @Arthur If f is injective but g is not injective, that means that g o f is not injective? If f is surjective but g is not surjective, that means that g o f is not surjective? – Jon D Jan 14 '18 at 17:26
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    @JonD I think it would be best if you post this as a different question, or search if this question is already answered in this site. – idok Jan 14 '18 at 17:29
  • @idok I can't post questions anymore... – Jon D Jan 14 '18 at 17:33

1 Answers1

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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.

Markus Scheuer
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