salut
1) domaine de def
=> x²-2x+2=0
delta<0 pas de solutions Df:R
2) f(x)=y
=> (x²+4x-4)/(x²-2x+2)-1
=> (x²+4x-4-x²+2x-2)/(x²-2x+2)
=> (6x-6)/(x²-2x+2)
=> (6(x-1))/(x²-2x+2)
tableau de signe
x -inf 1 +inf
x-1 - 0 +
x²-2x+2 + +
f(x)-y - 0 +
f<y de ] - inf ; 1 ]
f>y de [ 1 ; +inf [
3) f'(x)= u=x²+4x-4 u'= 2x+4
v= x²-2x+2 v'= 2x-2
formule ( (u'v-uv')/v²)
=>((2x+4)(x²-2x+2)-[(x²+4x-4)(2x-2)])/((x²-2x+2)²
=>(2x^3-4x+8-2x^3-6x²+16x-8)/(x²-2x+2)²
=>(-6x²+12x)/(x²-2x+2)²
=> (6x(-x+2))/(x²-2x+2)²
tableau
x -inf 0 2 +inf
f'(x) - 0 + 0 -
reste a mettre les flèches et les valeurs f(0) et f(2)
