Question

Ma ajutați cu acest exercitiu (E9) va rog ? 30 puncte

Answer 1

$\displaystyle G_f=\{\left(x,f(x)\right)|x\in\mathbb{R},f(x)=ax+b\}$

a)

$G_f\cap Ox=\{A(2,0)\}\Rightarrow f(2)=0\Rightarrow2a+b=0\\G_f\cap Oy=\{B(0,6)\}\Rightarrow f(0)=4\Rightarrow b=4\\2a+4=0\Rightarrow a=-2\\f(x)=-2x+4$

b)

$G_f\cap Ox=\{A(3a-1,0)\}\Rightarrow f(3a-1)=0\Rightarrow a(3a-1)+b=0\\G_f\cap Oy=\{B(0,4)\}\Rightarrow f(0)=4\Rightarrow b=4\\a(3a-1)+4=0\Rightarrow 3a^2-a+4=0\\\Delta=49\\\displaystyle a_{1,2}=\frac{1\pm7}{6}, a1=\frac{4}{3}, a2=-1\\f(x)=\frac43x+4=-x+4$

c) $G_f\cap Ox=\{A(7+2a,0)\}\Rightarrow f(7+2a)=0\Rightarrow a(7+2a)+b=0\\G_f\cap Oy=\{B(0,-3a)\}\Rightarrow f(0)=-3a\Rightarrow b=-3a\\a(7+2a)-3a=0\Rightarrow2a^2+7a-3a=0\Rightarrow2a^2+4a=0|:2\Rightarrow a^2+2a=0\Rightarrow a(a+2)=0\Rightarrow a=0\text{ sau }a=-2\\a=0\Rightarrow b=0\\a=-2\Rightarrow b=6\\f(x)=0=-2x+6$