Question

fie functiea f:R-R f(x) =3x-1 determinati punctul de pe grafic ce are a)ordonata egala cu -4 c)abcisa egala cu -2 b) coordonatele egala​

Answer 1

$f:\mathbb{R}\rightarrow\mathbb{R} \: \: \: ,f(x)=3x-1$

$a)Fie\:A(x_{A},4) \: \in \: G_{f} = > f(x_{A}) = 4$

$f(x_{A}) = 4$

$3x_{A} - 1 = 4$

$3x_{A} = 4 + 1$

$3x_{A} = 5$

$x_{A} = \frac{5}{3}$

$= > A(\frac{5}{3},4)$

$b)Fie\:B(-2,y_{B})\: \in\:G_{f}=>f(-2)=y_{B}$

$f(-2)=y_{B}$

$3 \times ( - 2) - 1 = y_{B}$

$y_{B} = - 6 - 1$

$y_{B} = - 7$

$= > B(-2,-7)$

$c)C(x,f(x))\:\in\:G_{f} = > x = f(x)$

$f(x) = x$

$3x - 1 = x$

$3x - x = 1$

$2x = 1$

$x = \frac{1}{2}$

$f( \frac{1}{2} ) = 3 \times \frac{1}{2} - 1 = \frac{3}{2} - \frac{2}{2} = \frac{1}{2}$

$= > C( \frac{1}{2} , \frac{1}{2} )$