Answer :

In order to determine if g = {(1, 1), (2, 3), (3, 5), (4, 7)} represents a function or not, we need to validate if g satisfies the condition of a relation to be a function.


A relation f from a set A to a set B is said to be a function if every


element of set A has one and only one image in set B.


By definition of function we can say that no two distinct ordered pairs in a function have the same first element.


We have,


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


we observe that each first element of ordered pairs is related to only one element.


Hence, g is a function.


Given,


g(x) = α x + β and g(1) = 1


α + β = 1 ……(i)


g(2) = 3, we get


α 2 + β = 3 ……(ii)


g(3) = 5, we get


α 3 + β = 5 ……(iii)


g(4) = 7, we get


α 4 + β = 7 ……(iv)


Solve any 2 equations from (i),(ii),(iii) and (iv) to find two unknowns α and β


On solving (i) and (ii), we get


α = 2 and β = -1


Hence, the function g(x) = 2x – 1


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