Let f= {(1,1), (2,3) , (0, -1) , (-1 ,-3)} be a linear function from z into z . find f (x)?

f(x) = 2x-1,

Let f(x) =y

Let y=mx+c, since it is a linear function.

Now, m= (y2-y1) /(x2-x1)

=>m=(3-1)/(2-1)

=>m=2,

Now, y=mx+c

=> 1= 2*1+c

=> c= -1

Hence f(x) =2x-1