Question

# 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.

Hint:

### An ordered pair is represented as (INPUT, OUTPUT)

A function from set A to the set B is a relation which associates every element of a set A to unique element of set B.

## The correct answer is: a = 2 and b = -1 .

### We have given a function from Z to Z

f = {(1,1), (2,3), (0,–1), (–1, –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(1) = 1

f(2) = 3

f(0) = -1

f(-1) = -3

i) (1,1)

f(1) = a (1) + b

1 = a + b

ii) (2,3)

f(2) = a (2) + b

3 = 2a + b

Subtract equation (i) from (ii)

2a – a + b – b = 3 – 1

a = 2

Putting this value in equation (i)

1 = 2 + b

b = 1 – 2

b = -1

Therefore, value of a = 2 and b = -1 .

And also we have given that

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

Putting this value in equation (i)

Therefore, value of a = 2 and b = -1 .

** **All functions are relations but all relations are not functions.

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