Maths-
General
Easy

Question

Given x = {(2, 7), (3, 9), (5, 13), (0, 3)} be a function from Z to Z defined by f(x) = ax + b for some integral a and b. What are the values of a and b?

The correct answer is: a = 2 and b = 3.


    We have given a function from Z to Z
    Given x = {(2, 7), (3, 9), (5, 13), (0, 3)}
    And also we have given that

    f(x) = ax + b
    We have to find the value of a and b .
    First of all if the f is a function then its points will satisfy f(x) = ax + b

    f(2) = 7

    f(3) = 9

    f(5) = 13

    f(0) = 3

    i) (2,7)

    f(2) = a (2) + b

    7 = 2a + b

    ii) (3,9)

    f(3) = a(3) + b

    9 = 3a + b
    Subtract equation (i) from (ii)

    3a – 2a + b – b = 9 – 7

    a = 2
    Putting this value in equation (i)

    7 = 2(2) + b

    b = 7 – 4

    b = 3
    Therefore, value of a = 2 and b = 3.

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