[tex]f:\mathbb{R}\rightarrow\mathbb{R}\:\:\:,f(x)=(2a+3)x-3a+2[/tex]
[tex]M(-1,-6)\:\in\:G_{f} < = > f( - 1) = - 6[/tex]
[tex]pt. \: a = 1 = > f(x) = (2 \times 1 + 3)x - 3 \times 1 + 2[/tex]
[tex]f(x) = 5x - 3 + 2 = 5x - 1[/tex]
[tex]f( - 1) = - 6[/tex]
[tex]5 \times ( - 1) - 1 = - 6[/tex]
[tex] - 5 - 1 = - 6[/tex]
[tex] - 6 = - 6 \: (A)[/tex]
Punctul de pe graficul funcției f care are abscisa egală cu un sfert din ordonată :
[tex]Fie \:P(x_{p},y_{P})\:\in\:G_{f}[/tex]
[tex]x_{P}=\frac{y_{P}}{4}[/tex]
[tex]P(x_{p},y_{P})\:\in\:G_{f}<=>f(x_{p})=y_{P}[/tex]
[tex]f(x)=5x-1=>f(x_{p})=5x_{p}-1[/tex]
[tex]5x_{p}-1=y_{P}[/tex]
[tex]5x_{p}=y_{p}+1[/tex]
[tex]x_{p}=\frac{y_{P}+1}{5}[/tex]
[tex]\frac{y_{P}}{4}=\frac{y_{P}+1}{5}[/tex]
[tex]5y_{P}=4(y_{P}+1)[/tex]
[tex]5y_{P}=4y_{P}+4[/tex]
[tex]5y_{P}-4y_{P}=4[/tex]
[tex]y_{P}=4[/tex]
[tex]x_{P}=\frac{y_{P}}{4}=\frac{4}{4}=1[/tex]
[tex]=>P(1,4)[/tex]
