[tex]f:\mathbb{R}\rightarrow\mathbb{R} \: \: \: ,f(x)=3x-1[/tex]
[tex]a)Fie\:A(x_{A},4) \: \in \: G_{f} = > f(x_{A}) = 4[/tex]
[tex]f(x_{A}) = 4[/tex]
[tex]3x_{A} - 1 = 4[/tex]
[tex]3x_{A} = 4 + 1[/tex]
[tex]3x_{A} = 5[/tex]
[tex]x_{A} = \frac{5}{3} [/tex]
[tex] = > A(\frac{5}{3},4)[/tex]
[tex]b)Fie\:B(-2,y_{B})\: \in\:G_{f}=>f(-2)=y_{B}[/tex]
[tex]f(-2)=y_{B}[/tex]
[tex]3 \times ( - 2) - 1 = y_{B}[/tex]
[tex]y_{B} = - 6 - 1[/tex]
[tex]y_{B} = - 7[/tex]
[tex] = > B(-2,-7)[/tex]
[tex]c)C(x,f(x))\:\in\:G_{f} = > x = f(x)[/tex]
[tex]f(x) = x[/tex]
[tex]3x - 1 = x[/tex]
[tex]3x - x = 1[/tex]
[tex]2x = 1[/tex]
[tex]x = \frac{1}{2} [/tex]
[tex]f( \frac{1}{2} ) = 3 \times \frac{1}{2} - 1 = \frac{3}{2} - \frac{2}{2} = \frac{1}{2} [/tex]
[tex] = > C( \frac{1}{2} , \frac{1}{2} )[/tex]
