AP EAMCET · Maths · Functions
How many functions \(f: \mathbf{Z} \rightarrow \mathbf{Z}\) are there such that \(f(x+y)=f(x)+f(y)\) for all \(x, y \in \mathbf{Z}\) ?
- A 1
- B 2
- C 3
- D Infinitely many
Answer & Solution
Correct Answer
(D) Infinitely many
Step-by-step Solution
Detailed explanation
\(F: z \longrightarrow z\) \(f(x+y)=f(x)+f(y)\) As sum of \(z\) integers always gives an integer so, there is no restriction and hence infinite such functions are possible.
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