Le nombre choisi est (-2) :
A = (2x + 1)^2
A = (2 * (-2) + 1)^2
A = (-4 + 1)^2
A = (-3)^2
A = 9
B = A - 1
B = 9 - 1
B = 8
C = B / 4
C = 8 / 4
C = 2
2) a) exprimer f(x) en fonction de x :
f(x) = [(2x + 1)^2 - 1] / 4
f(x) = [2x + 1 - 1][2x + 1 + 1] / 4
f(x) = (2x)(2x + 2) / 4
f(x) = 4x(x + 1) / 4
f(x) = x(x + 1)
b) calculer l'image de 3 :
f(3) = [(2 * 3 + 1)^2 - 1] / 4
f(3) = [(6 + 1)^2 - 1] / 4
f(3) = (7^2 - 1) / 4
f(3) = (49 - 1) / 4
f(3) = 48 / 4
f(3) = 12
c) f(-2) = -2(-2+1) = -2 * -1 = 2
f(-1) = -1(-1+1) = -1 * 0 = 0
f(0) = 0(0+1) = 0 * 1 = 0
f(1) = 1(1+1) = 1 * 2 = 2
f(2) = 2(2+1) = 2 * 3 = 6
f(3) = 3(3+1) = 3 * 4 = 12
f(4) = 4(4+1) = 4 * 5 = 20
d) les antécédents de 0 sont :
(-1) et 0
e) dans le tableau non, par le calcul :
f(x) = (-1/4)
x(x + 1) = (-1/4)
x^2 + x + 1/4 = 0
(x + 1/2)^2 = 0
x + 1/2 = 0
x = - 1 / 2
