Is g = {(1, 1), (2, 3), (3, 5), (4, 7)} a function? If g is described by g (x) = α x + β, then what value should be assigned to α and β.

Question

Philoid · Accepted 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