Question

Is $g=\{(1,1),(2,3),(3,5)(4,7)\}$ $g\left(x\right)=\alpha x+\beta ,$then what values should be assigned to $\alpha$ and $\beta$ ? find $\alpha +2\beta$

Answer 1

$\alpha =2,\beta =-1.$ Domain $A=1,2,3,4$ Range $B=1,3,5,7$ Every element of domain has a unique image in B and hence g is a function .Now $g\left(x\right)=\alpha x+\beta$ but $g\left(2\right)=3,g\left(3\right)=5.$ $\therefore 2=2\alpha +\beta$ and $5=3\alpha +\beta$ $\therefore \alpha =2,\beta =-1$