Dm (fonction linéaires et affines ) Bonsoir g besoin d'aide je ne comprend absolument rien.. J'ai essayer avec mes cours d'avancer un peu mais bon.. Dm en pièce

Exercice 1
1. a) f : x ->-2,5x = -5x/2
b) f(6) = -5*6/2 = -5*3 = -15
f(-3.5) = -5*-3,5/2 = 8,75

c) f(x) = 10
-5x/2 = 10
-5x = 20
x = -20/5
x = -4

f(x) = 5/3
-5x/2 = 5/3
-5x = 2*5/3
x = -2*5/3*5 = -2/3

2. a) f : x -> 7x/3 (ou (7/3)x)
b) f(2.4) = 7*2.4/3 = 5,6
f(-3/5) = (7/3)(-3/5) = -7/5

c) f(x) = 14
7x/3 = 14
7x = 14*3
x = 3*14/7
x = 6

f(x) = 5/3
7x/3 = 5/3
7x = 5
x = 5/7

3. a) f(x) = -3x
b) f(-5/6) = -3*-5/6 = 5/2
f(-0.7) = -3*-0.7 = 2,1

c) f(x) = -5
-3x = -5
x = 5/3

f(x) = -1/7
-3x = -1/7
x = 3/7

4. a) f: x -> -4x
b) f: x -> (-5/3)x
c) f(8) = 12 f: x -> (3/2)x
d) f: x -> (-5/6)x
e) f: x -> -3x
f) V8/V18 = v8*v18/V18² = V144/18 = 12/18 = 2/3 f: x -> (2/3)x

5.
a) coef = 7/5 : f(x) = (7/5)x
7x/5 =2.1
x = 2.1*5/7 = 0.3*5 = 1.5
f(-3) = -21/5 = -4,2
f(4) = 28/5 = 5,6

b) coef = -4/3 f(x) = (-4/3)x
f(x) = 4,4
-4x/3 = 4,4
x = -4.4*3/4 = -1.1*3 = -3,3
f(-3/7) = 4/7
-4x/3 = 1
x = -3/4

Exercice 2
1. l'image du nombre 2 est -1
2. l'image du nombre -1 est 0,5
3. L'image est 2 pour le nombre 4
4. L'image est -1 pour le nombre 2
5. le coefficient de cette fonction est -0,5 ou -1/2
6. f(7) = 7*-1/2 = -7/2 = -3,5 (* signifie multiplié par)
f(-5/4) = -5/4 * -1/2 = 5/8
7. f(7) = -3,5 donc il est vrai que le point de coordonnées est sur la droite (d)
8. Calcul de x pour le point appartenant à (d) et de coordonnées (x;14)
f(x) = -x/2
f(x) = 14
-x/2 = 14
-x = 14*2 = 28
x = -28

Calcul de y pour le point appartenant à (d) et de coordonnées (10;y)
f(10) = y
f(10) = -10/2
y = -10/2 = -5

Exercice 3
1.
a) f(6) = 2*6-5 = 12-5 = 7
f(-3,5) = 2*3,5-5 = 7-5 = 2
f(-7/4) = 2*-7/4 -5 = 2*-7/(2*2) -5 = -7/2 -5*2/2 = -7/2 - 10/2 = -17/2 = -8,5

b) f(x) = 11
2x-5= 11
2x = 11+5
2x = 16
x = 8

f(x) = -5
2x-5= -5
2x = 0
x = 0

c) f(x) = x
2x-5= x
2x-x = 5
x = 5

2. g(x) = 2x/3 + 3
a) 2.4 = 12/5
g(12/5) = 2/3*12/5 + 3 = 24/15 + 3*15/15 = 24/15+45/15 = 69/15 = 23/5
g(-3) = 2*-3/3 +3 = -2+3 = 1
g(-6/7) = 2/3 * -6/7 +3 = 2*-2/7 +3*7/7 = -4/7+21/7 = 17/7

b) g(a) = 3
2a/3+3=3
2a/3 = 3-3
2a/3 = 0
a = 0

g(b) = 1/3
2b/3+3 = 1/3
2b+3*3 = 1
2b = 1-9
2b = -8
b = -4

g(x) = 0
2x/3+3 = 0
2x/3 = -3
2x = -3*3
2x = -9
x = -9/2 ou -4,5

3. h(x) = x/6+ 2/3 = x/6+4/6 = (x+4)/6
a)
f(-6) = -6/6 + 2/3 = -3/3+2/3 = -1/3
f(x) = 1
(x+4)/6 = 1
x+4 = 6
x = 6-4 = 2

f(4/3) = 1/6 * 4/3 +2/3 = 4/(2*3*3) +2/3 = 2/9 + 6/9 = 8/9
f(x) = 7/6
(x+4)/6 = 7/6
x+4 = 7
x = 7-4 = 3

f(0) = 2/3
f(x) = 0
(x+4)/6 = 0
x+4 =0
x = -4

4.k(x) = xV3+1 (V se lit racine de)
a) k(1) = V3+1
k(-5V3) = -5V3*V3 + 1 = -5*3+1 = -15+1 = -14
k(V12) = V12*V3 +1 = V(12*3)+1 = V36+1 = 6+1 = 7

b) k(x) = V3
xV3+1 = V3
xV3 = V3-1
x = (V3-1)/V3
x = V3(v3-1)/(v3*V3)
x = 3/3-V3/3
x = 1-V3/3
Je trouve pas mieux ??