Q. 165.0( 1 Vote )

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 :

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


To find: whether g is a function, and also to find the values of α and β


Explanation: the given relation is g = {(1, 1), (2, 3), (3, 5), (4, 7)}


Here for every element in the domain has the unique image.


And a relation is said to be function if every element of one set has one and only one image in other set.


So g is a function.


Now given the relation g = {(1, 1), (2, 3), (3, 5), (4, 7)} as


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)


Now consider other ordered pair (2, 3), g (x) = αx + β, becomes


g (2) = α(2) + β = 3


2α + β = 3


Now substituting value of α from equation (i), we get


2(2) + β = 3


β = 3-4 = -1


Now substituting the value of β in equation (i), we get


α = 1-β = 1-(-1) = 2


Hence the values 2 and -1 should be assigned to α and β to satisfy the given condition g (x) = αx + β, i.e., g (x) = 2x-1


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