UPSC NDA Math Model Paper 3

The given relation is g = {(1, 1), (2, 3), (3, 5), (4, 7)} with domain A = {1, 2, 3, 4} and range B = {1, 3, 5, 7}.
∴ g(1) = 1, g(2) = 3, g(3) = 5 and g(4) = 7.
If g(x) = ax + b, we can say that:
g(1) = 1
⇒ a + b = 1 ...(1)
g(2) = 3
⇒ 2a + b = 3 ...(2)
Subtracting equation (1) from equation (2), we get a = 2 and therefore b = -1.