Answer:
[tex]G[/tex] is not function. The reason is that it is not one-to-one.
Step-by-step explanation:
A function is a mapping that is also one-to-one.
[tex]G[/tex] is indeed a mapping; it takes an input and relates it to one or more outputs.
- Input: [tex]1[/tex], output:
- Input: [tex]1[/tex], output: [tex]2[/tex].
- Input: [tex]1[/tex], output: [tex]3[/tex].
- Input: [tex]1[/tex], output: [tex]4[/tex].
A mapping is one-to-one if and only if each input is mapped to only one output. [tex]G[/tex] is not one-to-one because it maps the input [tex]1[/tex] to four different outputs. Hence, [tex]G[/tex] isn't a function.
