f(x) = (3 x - 1)/(x - 3) définie sur R - {3}
g(x) = - x² + 4 x - 3
1) calculer les images de 3 +√5 et de 7/3 par f
f(3+√5) = (3(3+√5) - 1)/(3+√5 - 3) = 8 + 3√5)/√5 = √5(8+3√5)/5
= 8√5 + 3*5)/5 = 15 + 8√5)/5 = 3 + (8/3)√5
f(7/3) = (3 (7/3) - 1)/(7/3 - 3) = 6/(- 2/3) = - 18/2 = - 9
Calculer g(-2) et g(1 - √2)
g(-2) = - (-2)² + 4 (-2) - 3 = - 4 - 8 - 3 = - 15
g(1-√2) = - (1-√2)² + 4(1 -√2) - 3 = - (1 - 2√2 + 2) + 4 - 4√2 - 3
= - 3 + 2√2 + 4 - 4√2 - 3 = - 2 - 2√2 = - 2(1 + √2)
