# Thread: Set Theory-Finding the Relative Complement of Two Functions

1. ## Set Theory-Finding the Relative Complement of Two Functions

My question is this:
How do you find the relative complement between two functions?

f(x)=x+2 {3,4,5,6,7...}
f1(x)=3x {3,6,9,12...}

{x+2\3x}

Should give you the sequence: {4,5,7,8...}

Is it possible to find a new function that will predict this sequence?

2. Originally Posted by joeday
My question is this:
How do you find the relative complement between two functions?

f(x)=x+2 {3,4,5,6,7...}
f1(x)=3x {3,6,9,12...}

{x+2\3x}

Should give you the sequence: {4,5,7,8...}

Is it possible to find a new function that will predict this sequence?
the answer is: $g(x)=3\left[\frac{x+2}{2}\right] + (-1)^{x+1}, \ \ x = 1,2,3, \ ... ,$ where $[a]$ is the integer part of $a.$

that was quite easy to find if you note that the elements of the sequence are in the form $3k \pm 1.$