Let f = {(1,1),(2,3),(0,-1),(-1,-3)} be linear function from Z into Z . Find f (x)

Let f = {(1,1),(2,3),(0,-1),(-1,-3)} be linear function from Z into Z

1.	Let f = {(1,1),(2,3),(0,-1),(-1,-3)} be linear function from Z into Z . Find f (x)
Answer» Let the linear function from Z into Z be\xa0{tex}f\\left( x \\right) =ax+b{/tex}Given\xa0{tex}f\\left( 1 \\right) =1,f\\left( 2 \\right) =3,f\\left( 0 \\right) =-1,f\\left( -1 \\right) =-3{/tex}Now\xa0{tex}f\\left( 1 \\right) =1\\Rightarrow a+b=1\\\\ f\\left( 0 \\right) =-1\\Rightarrow 0+b=-1\\Rightarrow b=-1{/tex}Substituting\xa0{tex}b=-1{/tex}\xa0in\xa0a+b=1 we get\xa0a-1 =1\xa0{tex}\\Rightarrow{/tex}a=1+1=2So we have a = 2 and\xa0{tex}b=-1{/tex}Hence the linear function from Z into Z is\xa0{tex}f\\left( x \\right) =2x-1{/tex}