1.

Is g = {(1, 1), (2, 3), (3, 5), (4, 7)} a function? Justify. If this is described by the relation g (x) = αx + β, then what values should be assigned to α and β?

Answer»

Answer is Yes, 

values should be α = 2 , β = −1

Explanation: Given that, g = {(1,1),(2,3),(3,5),(4,7)}
Here,each element of domain has unique image. So,g is a function .
Now given that, g(x) = αx+β
g(1) = 1 
⇒ α+β = 1
g(2) = 3
⇒ 2α+β = 3
Solving (i) and (ii), we get   
α = 2, β = -1
∴ g(x) = 2x - 1
above function satisfies (3,5) and (4,7)


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