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