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  • Is g = \{ (1, 1), (2, 3), (3, 5), (4, 7) \} a function? If g is described by g (x) = \alpha x + \beta , then what value should be assigned to \alpha and \beta .\\

Is g = \{ (1, 1), (2, 3), (3, 5), (4, 7) \}    a function? If g is described by g (x) = \alpha x + \beta   , then what value should be assigned to   \alpha\: \: and\: \: \beta   .

Answers (1)

Here,g = \{ (1, 1), (2, 3), (3, 5), (4, 7) \}

Here, each and every element of a domain has a unique image. Therefore, g is a function.

Also, g (x) = \alpha x + \beta

Therefore, 

\\g(1) = \alpha (1) + \beta = 1\\ \alpha + \beta = 1 \ldots \ldots .. (1)\\

Similarly,

g(2) = \alpha (2) + \beta = 2 \alpha + \beta = 3 \ldots \ldots .. (2)\\

By solving (1) and (2), we get

\alpha = 2 and \beta = -1\\

Therefore, g (x) = 2x - 1
 

Posted by

infoexpert22

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