RS Aggarwal - Mathematics

Book: RS Aggarwal - Mathematics

Chapter: 3. Functions

Subject: Maths - Class 11th

Q. No. 11 of Exercise 3A

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11

Let f = {(0, -5), (1, -2), (3, 4), (4, 7)} be a linear function from Z into Z. Write an expression for f.

Given that: f = {(0, -5), (1, -2), (3, 4), (4, 7)} be a function from Z to Z defined by linear function.

We know that, linear functions are of the form y = mx + b


Let f(x) = ax + b, for some integers a, b


Here, (0, -5) f


f(0) = -5


a(0) + b = -5


b = -5 …(i)


Similarly, (1, -2) f


f(1) = -2


a(1) + b = -2


a + b = -2


a + (-5) = -2 [from (i)]


a = -2 + 5


a = 3


f(x) = ax + b


= 3x + (-5)


f(x) = 3x - 5


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