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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.

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

Subtract equation (i) from (ii)

Putting this value in equation (i)

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

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