Question

Let $g\left(1\right)=1$ and $g\left(2\right)=3$ , if $g\left(x\right)$ is described by the formula$g\left(x\right)=ax-b$, then the value of $a$ and $b$ is?

Answer 1

Determine the values of $\mathbf{a}\mathbf{}\mathbf{and}\mathbf{}\mathbf{b}$:

$g\left(x\right)=ax-b$

$$\begin{gathered} \Rightarrow g\left(1\right)=a\left(1\right)-b=1\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{\left(}\mathit{i}\mathbf{\right)} \\ \Rightarrow g\left(2\right)=a\left(2\right)-b=3\mathbf{}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{\left(}\mathit{i}\mathit{i}\mathbf{\right)} \end{gathered}$$

Subtracting $\left(i\right)$ from $\left(ii\right)$ we get,

$$\begin{gathered} \Rightarrow 2a-b-(a-b)=3-1 \\ \Rightarrow 2a-b-a+b=2 \\ \Rightarrow a=2 \\ nowa-b=1 \\ \Rightarrow 2-b=1 \\ \Rightarrow b=1 \end{gathered}$$

Hence, the value of $a$ is $2$ and $b$is $1$