EDB — 08Y

Exercises

1. [08Y](Proposed on 2022-12) Let \(I,J⊆ ℝ\) and let \(f:I→ J\) be given by \(f(x)=\sin (x)\). By choosing \(I=ℝ\) or \(I=[0,𝜋/2]\) or \(I=[-𝜋/2,𝜋/2]\), and choosing \(J=ℝ\) or \(J=[-1,1]\), say for which choices \(f\) is surjective, and for which it is injective.

   (This exercise is to make you ponder about the difference between ”formula” and ”function.”.)