Question

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 1

According to the question,

g = {(1, 1), (2, 3), (3, 5), (4, 7)}, and is described by relation g (x) = αx + β

Now, given the relation,

g = {(1, 1), (2, 3), (3, 5), (4, 7)}

g (x) = αx + β

For ordered pair (1,1), g (x) = αx + β, becomes

g (1) = α(1) + β = 1

⇒ α + β = 1

⇒ α = 1 – β …(i)

Considering ordered pair (2, 3), g (x) = αx + β, becomes

g (2) = α(2) + β = 3

⇒ 2α + β = 3

Substituting value of α from equation (i), we get

⇒ 2(2) + β = 3

⇒ β = 3 – 4 = – 1

Substituting value of β in equation (i), we get

α = 1–β = 1–(–1) = 2

Now, the given equation becomes,

i.e., g (x) = 2x–1