Question

Suppose \(A=\\{0,1,2,3,4\\}, B=\\{2,3,4,5\\}\) and \(f=\\{(0,3),(1,3),(2,4),(3,2),(4,2)\\} .\) State the domain and range of \(f .\) Find \(f(2)\) and \(f(1)\)

Short answer

The domain of function \(f\) is \(\{0,1,2,3,4\}\), and the range of function \(f\) is \(\{2,3,4\}\). The value of \(f(2)\) is 4 and the value of \(f(1)\) is 3.

Step-by-step solution

Identify the Domain

The domain, \(D(f)\), of \(f\) is the set of all first elements in the ordered pairs. Looking at \(f=\{(0,3),(1,3),(2,4),(3,2),(4,2)\}\), the domain is \(D(f) = \{0,1,2,3,4\}\).

Identify the Range

The range, \(R(f)\), of \(f\) is the set of all second elements in the ordered pairs. Looking at \(f=\{(0,3),(1,3),(2,4),(3,2),(4,2)\}\), the range is \(R(f) = \{2,3,4\}\).

Find \(f(2)\) and \(f(1)\)

To find \(f(2)\), we look at the ordered pairs and find the pair where the first element is 2, which is the pair (2,4). Thus, \(f(2)=4\). Similarly, to find \(f(1)\), we look at the ordered pairs and find where the first element is 1, which is the pair (1,3). Thus, \(f(1)=3\).