Question

Funkcja liniowa Zad 1, 3, 4, 5, 6

Answer 1

1.
y=ax+b
a+b=4
-a+b=3
--------- +
2b=7
b=3,5
a+3,5=4
a=0,5
Odp. y=0,5x+3,5
3.
a1=a2
a=-1/8
y=-1/8x+b
-1/8*(-4) + b=-1
1/2 + b=-1
b=-1,5
Odp. y=-1/8 x - 1,5
4.
a1*a2=-1
p*3/(2p-1) = -1  /*(2p-1) , p≠1/2
3p=-(2p-1)
3p=-2p+1
3p+2p=1
5p=1
p=1/5
5.
a=tg150° = tg(180°-35°) = -tg30° = -√3/3
y=-x+b
-√3/3*(-3)+b = -1
√3+b=-1
b=-1-√3
Odp. y= -x - 1-√3.
6.
f(x)=-3x+5
-3x+5=0
-3x=-5  /:(-3)
m.z. x=5/3
g(x)=2/3 x+4/3
2/3x+4/3=0
2/3x=-4/3  /:(2/3)
x=-4/3*3/2
m.z. x= - 2
-3x+5 > 2/3x+4/3   /*3
-9x+15 > 2x+4
-9x-2x > 4-15
-11x > -11  /:(-11)
x<1
f(x)>g(x) dla x∈(-∞, 1)