Exercise 4:

Let \(f\) be the function from the set \(\{1, 2, 3, 4, 5\}\) into itself defined by:

• \(f(1) = 4, \quad f(2) = 1, \quad f(3) = 2, \quad f(4) = 2, \quad f(5) = 3\).

Determine:

• \(f(A) \text{ when } A = \{2\}, \quad A = \{1, 3, 4\}\).
• \(f^{-1}(B) \text{ when } B = \{3\}, \quad B = \{1, 2, 3\}\).

Exercise 5:

Are the following functions injective, surjective, bijective?

• \(f : \mathbb{Z} \to \mathbb{Z}, \quad n \mapsto 2|n| + 1\).
• \(g : \mathbb{R} \to \mathbb{R}, \quad x \mapsto -\frac{3}{2}x + 4\).
• \(h : \mathbb{R} \setminus \{1\} \to \mathbb{R}, \quad x \mapsto \frac{x+1}{x-1}\).