Exactly how many functions \(f: Q \rightarrow Q\) exist such that \(f(x+y)=f(x)+f(y)\) and \(f(x y)\)…
Exactly how many functions \(f: Q \rightarrow Q\) exist such that \(f(x+y)=f(x)+f(y)\) and \(f(x y)\) \(=f(x) f(y)\) for all \(x, y \in Q\) ?
- One
- Two
- Three
- Infinitely many
Solution
These functions are simultaneously satisfy for \(f(x)=x\) and \(f(x)=0 \forall x \in \mathbf{Q}\)
Hecne, option (b) is correct.
Asked in: AP EAMCET 2020 (18 Sep Shift 2)
Practice more Functions questions on Aicharya