Section 1.3: Functions

Check the injectivity and surjectivity of the following functions:

1. \(f : \mathbb{N} \to \mathbb{N}\) given by \(f(x) = x^2\)
   
2. \(f : \mathbb{Z} \to \mathbb{Z}\) given by \(f(x) = x^2\)
   
3. \(f : \mathbb{R} \to \mathbb{R}\) given by \(f(x) = x^2\)
   
4. \(f : \mathbb{N} \to \mathbb{N}\) given by \(f(x) = x^3\)
   
5. \(f : \mathbb{Z} \to \mathbb{Z}\) given by \(f(x) = x^3\)