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Is $g=\{(1,1),(2,3),(3,5),(4,7)\}$ a function ? If this is described by the formula $g(x)=\alpha x+\beta$, then what values should be assigned to $\alpha$ and $\beta$ ?
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As $\alpha=2, \beta=-1$
Domain $\mathrm{A}=\{1,2,3,4\}$
Range $\mathrm{B}=\{1,3,5,7\}$
Every element of domain has a unique image in $\mathrm{B}$ and hence $g$ is a function. Now $g(x)=\alpha x+\beta$ but $g(2)=3, g(3)=5$ $\therefore \quad 2=2 \alpha+\beta$ and $5=3 \alpha+\beta$ $\alpha=2, \beta=-1$
Domain $\mathrm{A}=\{1,2,3,4\}$
Range $\mathrm{B}=\{1,3,5,7\}$
Every element of domain has a unique image in $\mathrm{B}$ and hence $g$ is a function. Now $g(x)=\alpha x+\beta$ but $g(2)=3, g(3)=5$ $\therefore \quad 2=2 \alpha+\beta$ and $5=3 \alpha+\beta$ $\alpha=2, \beta=-1$
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