7. Five marks exercise problems I

1. Let \(f: A \rightarrow B\) be a function defined by \(f(x) = \frac{x}{2} - 1\), where \(A = \{2, 4, 6, 10, 12\}\), \(B = \{0, 1, 2, 4, 5, 9\}\). Represent \(f\) by

 

(i) set of ordered pairs

 

(ii) a table

 

(iii) an arrow diagram

 

(iv) a graph

 

 

2. Represent the function \(f = \{(1, 2), (2, 2), (3, 2), (4, 3), (5, 4)\}\) through

 

(i) an arrow diagram

 

(ii) a table form

 

(iii) a graph

 

 

3. Show that the function \(f: \mathbb{N} \rightarrow \mathbb{N}\) defined by \(f(x) = 2x - 1\) is one-one but not onto.