Let `f" "=" "{(1,1)," "(2," "3)," "(0, 1)," "(1," "3)}` be a function from Z to Z defined by `f(x)" "=" "a x" "+" "b` , for some integers a, b. Determine a, b.

Explanation

Given,f={(1,1),(2,3),(0,1),(−1,−3)} and f(x)=ax+b

Now,`(1,1)inf`

`f(1)=1⇒axx1+b=1`

⇒`a+b=1`

Also,`(0,−1)inf`

=`f(0)=−1⇒axx0+b=−1`

On substituting b=−1 in a+b=1

We obtain a+(−1)=1⇒a=1+1=2.
Thus, the respective values of a and b are 2 and -1.