Question

If $g\left(x\right)=\alpha x+\beta$ ,and $g=\left\{\right(1,1),(2,3),(3,5),(4,7\left)\right\}$ ,then the values of $\alpha ,\beta$ are:

Answer 1

Given that, $g=(1,1),(2,3),(3,5),(4,7)$

Here, each element of the domain has a unique image. So,$g$ is a function.
Now given that, $g\left(x\right)=\alpha x+\beta$

$g\left(1\right)=1$

⇒ $\alpha +\beta =1$

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

⇒ $2\alpha +\beta =3$

Solving (i) and (ii), we get

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

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

above function satisfies $(3,5)$ and $(4,7)$