Première S2 Exercices sur le chapitre 4 : E2. 2007 2008
E2 Savoir déterminer des fonctions composées.
P 17 n ° 36.
u ( x ) = 2x − 8 et v ( x ) = x²
v o u ( x ) = v ( u ( x ) ) = v ( 2x − 8 ) = ( 2x − 8 )² u o v ( x ) = u ( v ( x ) ) = u ( x² ) = 2x² − 8
u o u ( x ) = u ( u ( x ) ) = u ( 2x − 8 ) = 2 ( 2x − 8 ) − 8 = 4x − 16 − 8 = 4x − 24 v o v ( x ) = v ( v ( x ) ) = v ( x² ) = ( x² )² = x4.
p 17 n ° 37.
u ( x ) = 1
x et v ( x ) = 3x + 5
Du = * et Dv =
Dvou = { x ∈ / x ∈ Du et u ( x ) ∈ Dv }= { x ∈ / x ≠ 0 } = *
v o u ( x ) = v ( u ( x ) ) = v ( 1 x ) = 3
x + 5.
Duov = { x ∈ / x ∈ Dv et v ( x ) ∈ Du }= { x ∈ / 3x + 5 ≠ 0 } = − { - 5 3 }.
u o v ( x ) = u ( v ( x ) ) = u ( 3x + 5 ) = 5 x 31
+
Duou = { x ∈ / x ∈ Du et u ( x ) ∈ Du }= { x ∈ / x ≠ 0 } = *
u o u ( x ) = u ( u ( x ) ) = u ( 1 x ) =
x
11 = 1 × x 1 = x.
Dvov = { x ∈ / x ∈ Dv et v ( x ) ∈ Dv }= { x ∈ } =
v o v ( x ) = v ( v ( x ) ) = v ( 3x + 5 ) = 3 ( 3x + 5 ) + 5 = 9x + 15 + 5 = 9x +20.
