30)Let f: A→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.
Answer: A = {2, 4, 6, 10, 12}, B = {0, 1, 2, 4, 5, 9}, \(f(x) = \frac{x}{2} - 1\)
\(f(2) = \frac{2}{2} - 1 = 1 - 1 = 0\)
\(f(4) = \frac{4}{2} - 1 = 2 - 1 = 1\)
\(f(6) = \frac{6}{2} - 1 = 3 - 1 = 2\)
\(f(10) = \frac{10}{2} - 1 = 5 - 1 = 4\)
\(f(12) = \frac{12}{2} - 1 = 6 - 1 = 5\)
(i) Set of ordered pairs:
f = {(2,0), (4,1), (6,2), (10,4), (12,5)}
(ii) Table:
| x | 2 | 4 | 6 | 10 | 12 |
|---|---|---|---|---|---|
| f(x) | 0 | 1 | 2 | 4 | 5 |
(iii) Arrow diagram:
(iv) Graph:
