Is g = {(1, 1), (2, 3), (3, 5), (4, 7)} a function?
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

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