Question

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

Answer 1

Given that, $g=\left\{\right(1,1),(2,3),(3,5),(4,7\left)\right\}$
Here, each element of domain has unique image. So, g is a function.

Now given that, $g\left(x\right)=\alpha x+\beta$
$g\left(1\right)=\alpha +\beta \alpha +\beta =1...........\left(i\right)g\left(2\right)=2\alpha +\beta 2\alpha +\beta =\mathrm{3..........}\left(ii\right)$

From Eqs. (i)and (ii), $\alpha =2,\beta =-1$