Question

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

Answer 1

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)=1

$\Rightarrow \alpha +\beta =1$-------(1)

g(2)=34

$\Rightarrow 2\alpha +\beta =3$------(2)

On solving (1) and (2), we get,

$\alpha =2$, $\beta =-1$

$\therefore$ g(x)=2x-1