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Functions — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsFunctions3 Marks
Question
If a function g = {(1, 1), (2, 3), (3, 5), (4, 7)} is described by $\text{g(x)}=\alpha\text{x}+\beta\alpha\text{x}+\beta,$ then find the values of $\alpha$ and $\beta.$
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Answer

We have,
A function g = {(1, 1), (2, 3), (3, 5), (4, 7)} is described by $\text{g(x)}=\alpha\text{x}+\beta$
As, g(1) = 1 and g(2) = 3
Therefore, $\alpha(1)+\beta=1$
$=\alpha+\beta=1\ ....(\text{i})$
and $\alpha(2)-\beta=3$
$2\alpha-\beta=3\ ....(\text{ii})$
(ii) - (i) we get
$2\alpha-\alpha=2$
$\alpha=2$
Substituting $\alpha=2$ in (i), we get
$2+\beta=1$
$\beta=1$

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