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Is g={(1,1),(2,3),(3,5,),(4,7)} a functi...

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 `alphaa n dbeta?`

Text Solution

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We have `={(1,1),(2,3),(3,5),(4,7),}`
Since, every element has unique image under g. So g is a function.
Now,`g(x)=alpha x+beta`
When x =1 then, `g(1)=alpha(1) +beta " " ....(i)`
`rArr 1=alpha+beta`
When x=2, then, `g(2)=alpha(2)+beta`
`rArr 3=2alpha+beta" " ....(ii)`
On solving Eqs. (i) and (ii), we get
`alpha=2,beta=-1`
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