Răspuns:
f(x)=ax+b
faci 2x-1=2
2x=2+1
2x=3
x=3/2
f(2*3/2-1)+f(2)+f(1)=3*3/2+6
f(2)+f(2)+f(1)=9/2+6
2f(2)+f(1)=9/2+6 =21/2 ecuatia 1
faci 2x-1=1 2x=2 x=1
f(2*1-1)+f(2)+f(1)=3*1+6
f(1)+f(2)+f(1)=3+6
2f(1)+f(2)=9 ec 2
Faci sistem din ec 1 si ec 2
{2f(2)+f(1)=21/2
{f(2)+2f(1)=9
Inmultesti prima ecuatie cu 2 si o scazi din prima
f(2)+2f(1)-4f(2)-2f(1)=9-21
-3f(2)= -12=>
f(2)=-12/(-3)=4
Inlocuiesti f(2) in prima ecuatie
2*4+f(1)=21/2
8+f(1)=21/2
f(1)=21/2-8
f(1)=(21-16)/2= 5/2
f(1)=5/2
Deci revii la relatia f(x) =ax+b
f(2)=2a+b=4
f(1)=a+b=5/2
Scazi f(1) din f(2)
2a+b-a-b=4-5/2
a=(8-5)/2= 3/2
2*3/2+b=4
3+b=4
b=4-3=1
Deci f(x)=3x/2+1
a) intersectia cu Ox f(x)=0
3x/2+1=0
3x/2= -1
x= -2/3 A(-2/3,0)
f(0)=3*0/2+1=0+1=1
B(0,1)
S-a format triunghiul dreptunghiv AOB
Aria =AO*OB/2=l-2/3l*1/2=2/3*1/2=1/3
Explicație pas cu pas:
