bonjour
f ( 1) = 10 et f ( 5) = 2
( 2 - 10 ) / ( 5 - 1) = - 8/4 = - 2
f ( 1) = 10
- 2 + b = 10 ⇔ b = 12
f (x) = - 2 x + 12
d'où f ( 5) = - 10 + 12 = 2
3) - 2 x + 12 = 10/3
- 6 x /3 + 36/3 = 10/3
- 6 x = 10 - 36
- 6 x = - 26
x = 26/6 = 13/2
A ( 13/2 ; 10/3 )
4) g (x) > 0
9 - ( x - 3 )² > 0
( 3 + x - 3 ) ( 3 - x + 3 ) > 0
x ( - x + 6 ) > 0
x > 0
- x + 6 > 0 ⇔ - x > - 6 ⇔ x < 6
6 ) g (x) > f (x)
9 - ( x - 3 )² > - 2 x + 12
9 - ( x² - 6 x + 9 ) > - 2 x + 12
9 - x² + 6 x - 9 > - 2 x + 12
- x² + 6 x + 2 x > 12 - 9 + 9
- x² + 8 x > 12
- x² + 8 x - 12 > 0
se factorise en ( - x + 6 ) ( x - 2 )
- x + 6 > 0 ⇔ - x > - 6 ⇔ x < 6
x - 2 > 0 ⇔ x > 2
