Question

determinati valorile reale ale variabilei X pentru care au loc relatiile f(x)=0, f(x)>0
f(x)<0, f(x)≥ 0, f(x)≤0, daca F:R→R
a) f(x)=3x+51; b)f(x)=2-8x.

Answer 1

a) f(x)=0
3x+51=0
3x=-51
x=-51/3
x=-17

f(x)>0
3x+51>0
3x>-51
x>-51/3
x>-17
x∈(-17,+∞)  deci poate lua valorile -16,-15,...0,1,2, ......pana la infinit

f(x)<0
x<-17
x∈(-∞,-17) deci poate lua valori de la -∞, inclusiv-18

f(x)≥0
x≥-17 deci poate lua valorile -17,-16.....pana la +∞
x∈[-17,+∞)

f(x)≤0
x≤-17
x∈(-∞,-17] 

b) f(x)=0
2-8x=0
-8x=-2     inmultim -1
8x=2
x=2/8
x=1/4

f(x)>0
x>1/4
x∈(1/4,+∞)

f(x)<0
x<1/4
x∈(-∞,1/4)

f(x)≥0
x≥1/4
x∈[1/4,+∞)

f(x)≤0
x≤1/4
x∈(-∞,1/4]