Chap 03 : Généralités sur les fonctions

DR
f D Rx D f(x)
f(x)x f
x f(x)
(O;−→ i , −→ j)f Cf
M(x;f(x))
x7−→ ax +b a b ∈R R
x7−→ x2R
x7−→ 1
xR∗
x7−→ cos(x)x7−→ sin(x)R
f f(x) = 1
√x+ 1
f x x + 1 >0Df
f]−1; +∞[

f I
f x ∈I f(−x) = f(x)
f(−x) = −f(x)
gRg(x) = x2+ 1
hR∗h(x) = 1
x
(O;−→ i , −→ j)f
CfO
O
1
1x
y
(O;−→ i , −→ j)
f Cf(Oy)

1
1x
y
f I T
f T x ∈I f(x+T) = f(x)
(O;−→ i , −→ j)f
T Cf
kT −→ i k
1
1x
y
T

f I
Df
(x1;x2)I x1< x2f(x1)< f(x2)
f I
Df
(x1;x2)I x1< x2f(x2)< f(x1)
I f I
I
O
f (x1)
x1x2
f (x2)
O
f (x2)
x1x2
f (x1)
f I Df
f x0I x ∈I
f(x)≤f(x0)
f x1I x ∈I
f(x)≥f(x1)
uRu(x)=1−(x−2)2f
R

D
f=g x ∈D f(x) = g(x)
f≤g x ∈D f(x)≤g(x)
f≥g x ∈D f(x)≥g(x)
f≤g CfCg
f≥g CfCg
f
M x ∈I f(x)≤M
m x ∈I f(x)≥m
M m x ∈I m ≤f(x)≤M
f g DfDg
D=Df∩Dg
f+g x 7−→ f(x) + g(x)
kf x 7−→ k×f(x)k∈R
f×g x 7−→ f(x)×g(x)
x D g(x)6= 0 f
gx7−→ f(x) g(x)
I
I
k f
k > 0f kf
k < 0f kf I
f g x Dgg(x)∈Dff(g(x))
f g f ◦g f g (f◦g)(x) = f(g(x))