[tex] f:\mathbb{R} \to \mathbb{R} , \ f(x)=-x+2\\ f(0)=-f(4)\implies 0+2=-(-4+2)\\ 2=-(-2)\implies 2=2 \iff \bold{Adev\breve{a}rat} [/tex]
[tex] G_f \cap Ox =A \implies f(x)=0\\ -x+2 =0\implies x=2 \iff A(2,0) \\ G_f \cap Oy= B \implies f(0)=y \\ 0+2=y \implies y=2 \iff B(0,2) [/tex]
C(0, -2) ⇒ AO= OC ⇒ ΔAOC dreptunchis isoscel ⇒ <OAC = 45°
B(0, 2) ⇒ AO=BO ⇒ ΔAOB dreptunghic isoscel ⇒ <OAB = 45°
⇒ < BAC =90° ⇒ ΔBAC dreptunghic isoscel
[tex] d(B,AC)=AC\\ AC=d=l\sqrt{2}=2\sqrt{2} \ u.m.\\\iff \bold{ d(B,AC) =2\sqrt{2} \ u.m.}[/tex]
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Punctul a)
[tex] f:\mathbb{R} \to \mathbb{R} , \ f(x)=-x+2\\ f(0)=-f(4)\implies 0+2=-(-4+2)\\ 2=-(-2)\implies 2=2 \iff \bold{Adev\breve{a}rat} [/tex]
Punctul b)
[tex] G_f \cap Ox =A \implies f(x)=0\\ -x+2 =0\implies x=2 \iff A(2,0) \\ G_f \cap Oy= B \implies f(0)=y \\ 0+2=y \implies y=2 \iff B(0,2) [/tex]
C(0, -2) ⇒ AO= OC ⇒ ΔAOC dreptunchis isoscel ⇒ <OAC = 45°
B(0, 2) ⇒ AO=BO ⇒ ΔAOB dreptunghic isoscel ⇒ <OAB = 45°
⇒ < BAC =90° ⇒ ΔBAC dreptunghic isoscel
[tex] d(B,AC)=AC\\ AC=d=l\sqrt{2}=2\sqrt{2} \ u.m.\\\iff \bold{ d(B,AC) =2\sqrt{2} \ u.m.}[/tex]