bonjour,
4-(x+1)²=2²-(x+1)²
[2+(x+1)][2-(x+1)=(2+x+1)(2-x-1)
(x+3)(1-x)
(x+3)(1-x)=(x+3)(1-x)
(+3-x²-3x)=-x²-2x+3
f(x)≥0
(x+3)(1-x)≥0
x -∞ -3 1 +∞
x+3 - 0 + +
1-x + + 0 -
(x+3)(1-x) - 0 + 0 -
f(x)≥0 x∈[-3;0]
f(x)<3
-x²-2x+3<3
-x²-2x<3-3
-x²-2x<0
-x(x+2)<0
x -∞ -2 0 +∞
-x + + 0 -
x+2 - 0 + +
-x(x+2) - 0 + 0 -
-x(x+2)<0 x ∈ ]-∞;-2[ ∪ ]0,+∞[
f(x)<3 x ∈ ]-∞;-2[ ∪ ]0;+∞[
