[tex]f:\mathbb{R}\rightarrow\mathbb{R} \: \: \: ,f(x)=\frac{3}{2}x+1[/tex]
[tex]A(0,1),B(4,7)[/tex]
[tex]a)A(0,1)\:\in\:G_{f}<=>f(0)=1[/tex]
[tex] \frac{3}{2} \times 0 + 1 = 1[/tex]
[tex]0 + 1 = 1[/tex]
[tex]1 = 1 \: (A)[/tex]
[tex]B(4,7)\:\in\:G_{f}<=>f(4)=7[/tex]
[tex] \frac{3}{2} \times 4 + 1 = 7[/tex]
[tex]3 \times 2 + 1 = 7[/tex]
[tex]6 + 1 = 7[/tex]
[tex]7 = 7 \: (A)[/tex]
[tex]c)AB=\sqrt{{(x_{B}-x_{A})}^{2}+{(y_{B}-y_{A})}^{2}}[/tex]
[tex]AB = \sqrt{ {(4 - 0)}^{2} + {(7 - 1)}^{2} } [/tex]
[tex]AB = \sqrt{ {4}^{2} + {6}^{2} } [/tex]
[tex]AB = \sqrt{16 + 36} [/tex]
[tex]AB = \sqrt{52} [/tex]
[tex]AB = 2 \sqrt{13} [/tex]
