Question

F= {(1,1) (2,3) (0,-1) (-1, -3)} be
function from Z to Z defined by f(x)=ax+b,
for some integers
a & b. Determine a and b

Answer 1

f={(1,1),(2,3),(0,−1),(−1,−3)}

f(x)=ax+b

(1,1)

⇒f(1)=1

⇒a×1+b=1

⇒a+b=1

(0,−1)

⇒f(0)=−1

⇒a×0+b=−1

⇒b=−1

a+(−1)=1

⇒a=1+1=2

Thus the respective values of a and b are 2 and −1