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Home  >>  CBSE XII  >>  Math  >>  Relations and Functions
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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 $\alpha\;and\;\beta.$

$\begin{array}{1 1} \alpha =1 \qquad \beta =-1 \\ \alpha =2 \qquad \beta =-1 \\ \alpha =2 \qquad \beta =-2 \\ \alpha =-1 \qquad \beta =-1 \end{array} $

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Toolbox:
  • We find values for $\alpha$ and $\beta$ such that $b=\alpha a+\beta$ for all or ordered pairs $(a,b) \in g$
$g=\{(1,1),(2,3),(3,5)(4,7)\}$ is a function
 
we see that
 
If $g(x)=2x-1$ is satisfied for all values of $x =\{1,2,3,4\}$
 
$g(1)=2 \times 1-1=1$
 
$g(2)=2 \times 2-1=3$
 
$g(3)=2 \times 3-1=5$
 
$g(4)=2 \times 4-1=7$
 
Hence $ \alpha =2 \qquad \beta =-1$

 

 

answered Mar 1, 2013 by meena.p
 

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