Let f : ℝ → ℝ be a function satisfying f(x + y) = f(x)f(y), ∀x, y ∈ ℝ and \(\lim _{x \rightarrow 0} f(x)=1\). Which of the following are necessarily true?
1
f is stricly increasing
2
f is either constant or bounded
3
f(rx) = f(x)r for every rational
4
f(x) ≥ 0, ∀ x ∈ ℝ