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Home » Is g = {(1, 1), (2, 3), (3, 5), (4, 7)} a function? Justify. If this is described by the relation, g (x) = αx + β, then what values should be assigned to α and β?
Is g = {(1, 1), (2, 3), (3, 5), (4, 7)} a function? Justify. If this is described by the relation, g (x) = αx + β, then what values should be assigned to α and β?
CBSE | Class 11 | Maths | NCERT Exemplar | Relations and Functions
Is g = {(1, 1), (2, 3), (3, 5), (4, 7)} a function? Justify. If this is described by the relation, g (x) = αx + β, then what values should be assigned to α and β?

Solution:

Provided,

\mathrm{g}=\{(1,1),(2,3),(3,5),(4,7)\}, and is described by relation \mathrm{g}) (\mathrm{x})=\boldsymbol{\alpha} x+\boldsymbol{\beta}

Now, given the relation,

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

g(x)=\boldsymbol{\alpha} x+\boldsymbol{\beta}

For ordered pair (1,1), \mathrm{g}(\mathrm{x})=\boldsymbol{\alpha} \mathrm{x}+\boldsymbol{\beta}, becomes

g(1)=\boldsymbol{\alpha}(1)+\boldsymbol{\beta}=1

\Rightarrow \boldsymbol{\alpha}+\boldsymbol{\beta}=1

\Rightarrow \alpha=1-\beta \ldots \dots \dots. (i)

Now consider the ordered pair (2,3), g(x)=\boldsymbol{\alpha} x+\boldsymbol{\beta}, becomes

g(2)=\boldsymbol{\alpha}(2)+\boldsymbol{\beta}=3

\Rightarrow 2 \boldsymbol{\alpha}+\boldsymbol{\beta}=3

When we substitute value of \boldsymbol{\alpha} from eq.(i), we have

\Rightarrow 2(2)+\boldsymbol{\beta}=3

\Rightarrow \boldsymbol{\beta}=3-4=-1

Substituting value of \boldsymbol{\beta} in equation (i), we get

\boldsymbol{\alpha}=1-\boldsymbol{\beta}=1-(-1)=2

So now, the provided equation becomes,
i.e., g(x)=2 x-1

i

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