Types Of Functions

For n even: . For n odd: .

f is injective: No two different inputs map to the same output. For example:

• If and are even or odd, the outputs .
• If is even and is odd, their outputs and are distinct.

Hence, f is injective.

f is surjective: Every natural number is an output of f:

• For odd k, , where is even.
• For even k, , where is odd.

Hence, f is surjective.

f is invertible: Since f is both injective and surjective, it is invertible. The inverse function is:

Thus, the function f satisfies properties (A), (C), and (D).

Answer:

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