1. Tardigrade
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  3. Mathematics
  4. If g= (1,1),(2,3),(3,5),(4,7) is a function described by the formula, g ( x )=α x +β then what values should be assigned to α and β ?

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

Relations and Functions

Solution:

$(1,1)$ satisfies $g(x)=\alpha x+\beta$
$ \therefore \alpha+\beta=1$
$(2,3)$ satisfies $g(x)=\alpha x+\beta$
$ \therefore 2 \alpha+\beta=3$
Solving the two equation, we get
$\alpha=2, \beta=-1$
It can be checked that other ordered pairs satisfy
$g(x)=2 x-1$