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 $\beta$.
Find $\alpha$ + $\beta$.

Answer 1

Since no two ordered pairs in $g$ have the same first component

So, $g$ is a function such that

$g\left(1\right)=1,g\left(2\right)=2,g\left(3\right)=5$ and $g\left(4\right)=7.$

If is given that $g\left(x\right)=\alpha x+\beta .$

Therefore,

$g\left(1\right)=1$ and $g\left(2\right)=3$

$\Rightarrow \alpha +\beta =1$ and $2\alpha +\beta =3$

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

$\therefore \alpha +\beta =2-1=1$