If f = {(1, 1), (2, 3), (0, - 1), (- 1, - 3)} be a function from Z to

1.	If f = {(1, 1), (2, 3), (0, - 1), (- 1, - 3)} be a function from Z to Z where Z is the set of integers such that f(x) = ax + b for some integers a, b then find the value of a and b ?1. a = 1 and b = 22. a = 3 and b = 23. a = - 2 and b = 14. a = 2 and b = - 1
Answer» Correct Answer - Option 4 : a = 2 and b = - 1 Calculation: Given: f = {(1, 1), (2, 3), (0, - 1), (- 1, - 3)} is a function from Z to Z where Z is the set of integers such that f(x) = ax + b for some integers a and b. As (1, 1) ∈ f ⇒ x = 1 and y = 1 will satisfy the equation y = f(x) = ax + b ⇒ a + b = 1 Similarly (2, 3) ∈ f ⇒ x = 2 and y = 3 will satisfy the equation y = f(x) = ax + b ⇒ 2a + b = 3 Now by solving the equations a + b = 1 and 2a + b = 3, we get a = 2 and b = - 1 Hence, option 4 is the correct answer.

If f = {(1, 1), (2, 3), (0, - 1), (- 1, - 3)} be a function from Z to Z where Z is the set of integers such that f(x) = ax + b for some integers a, b then find the value of a and b ?1. a = 1 and b = 22. a = 3 and b = 23. a = - 2 and b = 14. a = 2 and b = - 1

Answer» Correct Answer - Option 4 : a = 2 and b = - 1

Calculation:

Given: f = {(1, 1), (2, 3), (0, - 1), (- 1, - 3)} is a function from Z to Z where Z is the set of integers such that f(x) = ax + b for some integers a and b.

As (1, 1) ∈ f ⇒ x = 1 and y = 1 will satisfy the equation y = f(x) = ax + b ⇒ a + b = 1

Similarly (2, 3) ∈ f ⇒ x = 2 and y = 3 will satisfy the equation y = f(x) = ax + b ⇒ 2a + b = 3

Now by solving the equations a + b = 1 and 2a + b = 3, we get a = 2 and b = - 1

Hence, option 4 is the correct answer.

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