Question

Va roggg ajutati-ma , nu stiu cum se rezolva!! :((( Calculati aria triunghiului determinat de axa Ox si reprezentarile grafice ale functiilor f ,g : R⇒R urmatoare:
b) f(x) = x+3 si g(x) = -2x+2;
c) f(x) = -2x-5 si g(x) = x-3 ;
d) f(x) = -3x+1 si g(x) = 2x-7.

Answer 1

b) x+3=-2x+2 ( se egaleaza cele doua functii)
x+2x=2-3
3x=-1 
x=1/3
f(1/3)=-1/3+3(amplificam cu 3)=8/3 (adaugam in f(x) rezultatul obtinut)
=) I(8/3,4)
=)Aria=(Cateta1*Cateta2)/2=(8/3x4)/2=32/3/2=32/6=16/3 unitati de masura la a doua
c)-2x-5=x-3
-3x=-3+5
-3x=2
x=-2/3
f(2/3)=-2*(-2/3)-5=-4/3-4(amplificam cu 3)=-4/3-12/3=-16/3
=>I(-2/3,-16/3)
Aria= (-2/3*-16/3)/2=32/9/3=32/27 unitati de masura la patrat
d)-3x+1=2x+7
-5x=6
x=-6/5
f(-6/5)= 3* (-6/5) +1=-18/5 +1(amplificam cu 5)=18/5+5/5=23/5
=>I(-6/5, 23/5)
Aria=(-6/5*23/5)/2= -138/25/2=-138/50

Answer 2

b) f(x) = x+3 si g(x) = -2x+2;
f(x)=g(x)
 x+3=-2x+2
3x=-1
x=-1/3
f(x)=y
f(-1/3)=-1/3 +3
=-1+9/3
=8/3
A= (1/3 * 8/3 ) :2
A=4/9 u ^2

c) f(x) = -2x-5 si g(x) = x-3 ;
-2x-5=x-3
-3x=2
x=-2/3
y=-2 - 9/3
y=-11/3
A=22/9:2
A=11/9 u ^2 
c) -3x+1=2x-7. 
-5x=-8
x=8/5
y=16-35/5
y=19/5
A=(8/5 * 19/5 ) :2