Question

Urgent..va rog!dau coroana.

Answer 1

[tex]\it f(x)=ax+b \\\;\\ f(2)=3 \Rightarrow a\cdot2+b=3 \Rightarrow 2a+b=3 \Rightarrow b=3-2a\ \ \ \ \ (1) \\\;\\ f(-1) = 5 \Rightarrow a\cdot(-1)+b=5 \Rightarrow -a+b=5 \Rightarrow b=5+a\ \ \ \ (2) \\\;\\ (1),\ (2) \Rightarrow 5+a=3-2a \Rightarrow a+2a = 3-5 \Rightarrow a= - \dfrac{2}{3}\ \ \ \ (3) \\\;\\ (2),\ (3) \Rightarrow b = 5+(-\dfrac{2}{3}) = 5-\dfrac{2}{3} = \dfrac{13}{3} \\\;\\ \\\;\\ Deci, \ \ a = -\dfrac{2}{3},\ \ b = \dfrac{13}{3}.[/tex]

[tex]\it b)\ Pentru\ a=3,\ b=5 \Longrightarrow f(x)=3x+5 \\\;\\ Gf\cap Ox=A(x,\ 0) \\\;\\ A(x,\ 0) \in Gf \Rightarrow f(x)=0 \Rightarrow 3x+5=0 \Rightarrow \ x=-\dfrac{5}{3} \Rightarrow \\\;\\ \Rightarrow Gf \cap Ox = A\left(-\dfrac{5}{3},\ 0\right) \\\;\\ Gf\cap Oy=B(0,\ y) \\\;\\ B(0,\ y) \in Gf \Rightarrow f(0)=y \Rightarrow 3\cdot0+5=y \Rightarrow \ y=5 \Rightarrow \\\;\\ \Rightarrow Gf \cap Oy = B(0,\ 5) [/tex]

$\it \mathcal{A}_{AOB} = \dfrac{AO\cdot BO}{2} =\dfrac{\dfrac{5}{3}\cdot5}{2}=\dfrac{25}{6}\ u.\ a.$