Applications/Arithmétique

f:R→R
x7→ x2
f([−2,2]) f([−1,2])
f−1([0,3]) f−1([−1,3]) f−1([−2,−1])
f:E→F A ⊂E B ⊂F
f(A)∩B=fA∩f−1(B).
E, F f :E→F A, B ∈ P(E)
f(A∩B)⊂f(A)∩f(B)
f f(A)∩f(B)⊂f(A∩B)
E, F, G f :E→F g :F→G
g◦f g
g◦f f
f:R2→R3
(x1, x2)7→ f((x1, x2)) = (1, x1+x2, x1−x2)
f
f:R→C
x7→ 1+ix
1−ix
f(R) = U\ {−1}
f−1(R)
f:C∗→C
z7→ z+1
z
.
f
f(U)=[−2,2]
f−1(iR)
√2
f:R→Rf(x) = x2x≥0
2x2x < 0.
f
f|QfQ
Zx
y x ∼y x +y∼
∼R
x∼y⇐⇒ xey=yex,
xR
x
498 222
n7n+ 1 8
n7n+ 1
8
7 = 8 −1
10!
p k ∈J1, p−1Kpp
k
p np−n
p n np−1−1