Let f = {(1, 1), (2, 3), (0, - 1), (- 1, - 3)} be a function from Z to Z defined by f (x) = ax + b, for some integers a, b. Determine a, b

Solution:

It is given that

f = {(1, 1), (2, 3), (0, - 1), (- 1, - 3)} and f (x) = ax + b

(1, 1) ∈ f

⇒ f (1) = 1

⇒ a x 1 + b = 1

⇒ a + b = 1

(0, - 1) ∈ f

⇒ f (0) = - 1

⇒ a x 0 + b = - 1

⇒ b = - 1

On substituting b = - 1 in a + b = 1, we obtain

a + (- 1) = 1

a = 1 + 1

= 2

Thus, the respective values of a and b are 2 and - 1

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NCERT Solutions Class 11 Maths Chapter 2 Exercise ME Question 8

Let f = {(1, 1), (2, 3), (0, - 1), (- 1, - 3)} be a function from Z to Z defined by f (x) = ax + b, for some integers a, b. Determine a, b.

Summary:

Thus, the respective values of a and b are determined to be 2 and - 1