Question 37
Determine all functions $f: \mathbb{R} \rightarrow \mathbb{R}$ that simultaneously satisfy the conditions:
1) $|f(x)| \geq 1$ for every real number $x$.
2) $f(x+y)=\frac{f(x)+f(y)}{1+f(x) \cdot f(y)}$ for all real numbers $x$ and $y$.
1) $|f(x)| \geq 1$ for every real number $x$.
2) $f(x+y)=\frac{f(x)+f(y)}{1+f(x) \cdot f(y)}$ for all real numbers $x$ and $y$.