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Is `g={(1,1),(2,3),(3,5,),(4,7)}`a function? If this is described by the formula, `g(x)=alphax+beta,`then what values should be assigned to `alpha` and `beta?` |
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Answer» 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 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` `implies 2-2beta + beta=3` `implies 2 -beta=3` ` " " beta= -1` If `beta = -1,` then `alpha = 2` `alpha=2, beta = -1` |
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