Question

If the function f:N- N is defined as f(x) is equal to 3x+2 ,x belongs to N,then the pre-image of 29 is

Answer 1

Answer:

Step-by-step explanation:

f(x) = 3x+2

i) Find the images of 1,2,3

Image when x = 1,

f(1) = 3(1) + 2

= 3 + 2

= 5

Image when x = 2

f(2) = 3(2) + 2

= 6 + 2

= 8

Image when x = 3

f(3) = 3(3) + 2

= 9 + 2

= 11

Images of 1,2,3 = {5,8,11}

ii) Pre-images of 29,53

Pre-image when f(x) = 29

f(x) = 3x + 2

29 = 3x + 2

29 - 2 = 3x

3x = 27

x = 27

3

x = 9

Pre-image when f(x) = 53

f(x) = 3x + 2

53 = 3x + 2

53 - 2 = 3x

3x = 51

x = 51

3

x = 27

Pre-images of 29,53 = {9,27}

This is one to one function as one pre-image has only one image.