Question

Is $g=(1,1),(2,3),(3,5),(4,7)$ a function? If this is described by the formula $g\left(x\right)=\alpha x+\beta$, then value of $\alpha -\beta$ is _____.

Answer 1

Clearly, here $g\left(1\right)=1,,g\left(2\right)=3,g\left(3\right)=5,g\left(4\right)=7$

Thus, $g$ is a function.

Also, $g\left(x\right)=\alpha x+\beta$

Therefore

$\alpha +\beta =1,2\alpha +\beta =3,3\alpha +\beta =5,4\alpha +\beta =7$
Solving above equations we get $\alpha =2,\beta =-1$

Then $\alpha -\beta =3$.