Relations and Functions — Class 12 Maths Solution

It is given that,, $g = \{ (1,1),(2,3),(3,5),(4,7)\}$.

Here, each element of domain has unique image.

So, $g$ is a function. Now It is given that,, $g(x) = \alpha x + \beta$

$g(1) = \alpha + \beta$

$\alpha + \beta = 1$
…(i)
$g(2) = 2\alpha + \beta$

$2\alpha + \beta = 3$
…(ii)
From Eqs. (i) and (ii),

$2(1 - \beta ) + \beta = 3$

$\Rightarrow$ $2 - 2\beta + \beta = 3$

$\Rightarrow$ $2 - \beta = 3$

$\beta = - 1$

If $\beta = - 1$, then $\alpha = 2$

$\alpha = 2,\beta = - 1$