If a function g = {(1, 1), (2, 3), (3, 5), (4, 7)} is described by g(x) = αx + β, find the values of α and β.
Given:-
(i)g={(1, 1), (2, 3), (3, 5), (4, 7)}
(ii)g(x) = αx + β
For x=1 and αx + β
g(1)=α(1)+ β=1
⇒ α+ β=1
For x=2
g(2)=α(2)- β=3
⇒ 2α- β=3
Similarly with g(3) and g(4)
Using above value
α=2
β=1