Is `g={(1,1),(2,3),(3,5,),(4,7)}` a function? If this is described by the formula, `g(x)=alphax+beta,` then what values should be assigned to `alpha` and `beta?`

Explanation

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) =alpha x + beta `
`g(1)=alpha + beta`
`alpha + beta =1 " " ` ...(i)
`g(2)=2 alpha + beta`
`2 alpha + beta=3 " " `...(ii)
From Eqs. (i) and (ii),
`2(1 - beta) +beta =3`
`implies 2-2beta + beta=3`
`implies 2 -beta=3`
` " " beta= -1`
If `beta = -1,` then `alpha = 2`
`alpha=2, beta = -1`