Question

If g={(1,1),(2,3),(3,5),(4,7)} and g(x)=αx+β, the α and β are:
a)α=-2β=1
b)α=2β=-1
c)α=2β=1
d)none
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Answer 1

Answer:

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) = 34

⇒ 2α+β = 3

Solving (i) and (ii), we get

α = 2, β = -1

∴ g(x) = 2x - 1