Bonjour,
1)a• f(0) = 3 ; f(1) = 5 ; f(-4) = -5
g(0) = 0 ; g(1) = -1 ; g(-4) = 4
1)b• f(0) = 3 ; f(-4) = - 5 ; f(1) = 5
g(-3) = 3 ; g(5) = -5 ; g(-5) = 5
2) f(-1) = g(-1)
S = {-1}
3) f(x) = 2x + 3 et g(x) = -x
4)
Vérification :
• Question 1)a :
f(0) = 2×0 + 3 = 3 ; f(1) = 2×1 + 3 = 5 ; f(-4) = 2×(-4) + 3 = -5
g(0) = -0 = 0 ; g(1) = -1 ; g(-4) = -4
• Question 1)b :
f(x) = 3 => 2x + 3 = 3 => 2x = 0 => x = 0
f(x) = -5 => 2x + 3 = -5 => 2x = -8 => x = -4
f(x) = 5 => 2x + 3 = 5 => 2x = 2 => x = 1
g(x) = 3 => -x = 3 => x = -3
g(x) = -5 => -x = -5 => x = 5
g(x) = 5 => -x = 5 => x = -5
• Question 2 :
f(x) = g(x)
2x + 3 = -x
2x + x = -3
3x = -3
x = -3/3
x = -1
On a bien f(x) = g(x) pour x = -1.
