Question

Let = {(1,1), (2,3), (0, – 1), (– 1, – 3)} be a function from Z to Z defined
by () = + , for some integers , . Determine , and hence write
().

Answer 1

Step-by-step explanation:

f={(1,1),(2,3),(0,−1),(−1,−3)}

f(x)=ax+b

(1,1)∈f

⇒f(1)=1

⇒a×1+b=1

⇒a+b=1 .....(1)

(0,−1)∈f

⇒f(0)=−1

⇒a×0+b=−1

⇒b=−1

On substituting b=−1 in eqn (1), we get

a+(−1)=1

⇒a=1+1=2

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

Answer 2

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