Question

3. Let f = {(1, 1) (2, 3)(0,-1) be function
from 2 to z defined by f(x)= as+b
for integers a & b. Determine a&b.
7​

Answer 1

Answer:

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