Bonsoir
1)
a)
Cf. pièce jointe
b)
f(x) >= g(x)
S = ]-oo, -1] U ]0, 2]
2)
a)
f(x) - g(x) = 2/x - ( x-1 ) =2/x - x + 1
f(x) - g(x) = 2/x - x + 1
f(x) - g(x) = 2/x - x²/x + x/x
f(x) - g(x) = ( 2 - x² + x) / x
f(x) - g(x) = ( - x² + x + 2) / x CQFD
b) Développons :
(x + 1)(-x + 2) = -x² + 2x -x + 2 = -x² + x + 2 XQF
3)
a)
les solutions de (x + 1)(-x + 2) sont x=-1 ou x=2
-00 +00
-------------------|---------------- -1 ---------------- 2 -------------------
(x + 1) | - 0 + | +
(-x + 2) | + | + 0 -
(-x + 2) (x+1) | - | + | -
b)
-00 +00
----------------------|---------------- -1 -------0-------- 2 -----------------
(-x + 2) (x+1) | - 0 + 0 -
x | - - 0 + +
((-x + 2) (x+1)) /x | + 0 - || + 0 -
c) f(x)-g(x) >=0 ==> f(x) >= g(x)
S=]-oo; -1] dans ]-oo; 0[
4) Cf graphique ci joint
f(x)-g(x) >=0 ==> f(x) >= g(x)
S = ]-oo, -1] U ]0, 2] on retrouve la solution 1.b
S=]-oo; -1] dans ]-oo; 0[
