Fonction inverse et fonctions hommographiques, classe de seconde

f
]− ∞; 0[∪]0; +∞[
f(x) = 1
x
•]− ∞; 0[
•]0; +∞[
f(x)−∞ +∞
k &
xk
& k
•x1x20< x1≤x2
1
x1x2
x1
x1x2≤x2 x1x2
1
x2≤1 x1
]0; +∞[
•x1x2x1≤x2<0
1
x1x2
x1
x1x2≤x2 x1x2
1
x2≤1 x1
]0; +∞[
]− ∞; 0[ ]0; +∞[
x−∞ +∞
1
x

x f(−x) = −f(x)
(O;~ i;~ j)

a b c d c 6= 0 f(x) =
ax+b
cx+dx−d c
f x
f
f f(x) = 3x+2
−4x+5 f
−4x+ 5 = 0 −4x=−5x=5
4
5
4
f f R− {5
4}
(3x+ 2)(4x+ 1)
5x+ 3 = 0.
5x+ 3 = 0 5x=−3x=−3
5
−5
3
R − −5
3
(3x+2)(4x+1)
5x+3 = 0 (3x+ 2)(4x+ 1) = 0
3x+ 2 = 0 4x+ 1 = 0 x=−2
3x=−1 4
−2
3
−1
4
x2−2
3x−1= 0.
•3x−1 = 0 x=1
3

•
x2−2
3x−1=(x−√2)(x+√2) 3x−1
•
(x−√2)(x+√2) = 0
x=√2x=−√2
•
S={−√2; √2}