Cours ANAL Nu

f(x)=0
√a, a > 0.
n= 2

f(x)=0 f
f(x)=0
fR R D(f)Rα∈D(f)
f(x) = 0
f(α) = 0.

α
Ker(f) = {x∈D(f)/ f(x)=0}.
À
f(x) = ax2+bx +c, a, b c ∈R.
Ker(f)
Á
f(x) = sin(x), D(f) = R+.
f(x)=0
Ker(f) = {x∈R+/x =kπ, k = 0,1, ...}.
Â
f(x) = (sin( 1
x)x > 0,
0x≤0,
Ker(f) = R−∪ {x=1
kπ , k = 1, ...}.
α[a, b]α
[a, b]Ker(f)∩[a, b] = {α}
Ê
Ë
α
f(ox)
Àf(x) = x2−a a > 0D(f) = R
f

x∞ ∞
f0(x)
∞ ∞
f(x)
& %
−a
−4−2 0 2 4
0
5
10
15
x
f(x) = x2−2
a= 2
f
2
f(x)=0
(ox)f(x)=0
Á
(xlog(x) = 1,
D(f) = R+
∗,
log(x) = 1
x,
D(f) = R+
∗,
f1(x) = log(x)f2(x) = 1
x
(f1(x)−f2(x) = 0,
D=R+
∗,