Question

If a function g = {(1, 1), (2, 3), (3, 5), (4, 7)} is described by g(x) = $\alpha x+\beta$, then find the values of $\alpha$ and $\beta$. [NCERT EXEMPLAR]

Answer 1

We have,

A function g = {(1, 1), (2, 3), (3, 5), (4, 7)} is described by g(x) = $\alpha x+\beta$

$$\begin{gathered} \mathrm{As},g\left(1\right)=1\mathrm{and}g\left(2\right)=3 \\ \mathrm{So},\alpha \left(1\right)+\beta =1 \\ \Rightarrow \alpha +\beta =1.....\left(\mathrm{i}\right) \\ \mathrm{and}\alpha \left(2\right)+\beta =3 \\ \Rightarrow 2\alpha +\beta =3.....\left(\mathrm{ii}\right) \\ \left(\mathrm{ii}\right)-\left(\mathrm{i}\right),\mathrm{we}\mathrm{get} \\ 2\alpha -\alpha =2 \\ \Rightarrow \alpha =2 \\ \mathrm{Substituting}\alpha =2\mathrm{in}\left(\mathrm{i}\right),\mathrm{we}\mathrm{get} \\ 2+\beta =1 \\ \Rightarrow \beta =-1 \end{gathered}$$