Question:
Is g = {(1, 1), (2, 3), (3, 5), (4, 7)} a function? If g is described by g (x) = αx + β, then what value should be assigned to α and β.
Solution:
Given, g = {(1, 1), (2, 3), (3, 5), (4, 7)}
It’s seen that every element of domain has a unique image. So, g is function.
Now, also given that g (x) = αx + β
So, we have
g (1) = α(1) + β = 1
α + β = 1 …….. (i)
And, g (2) = α(2) + β = 3
2α + β = 3 …….. (ii)
Solving (i) and (ii), we have
α = 2 and β = -1
Therefore, g (x) = 2x – 1