急 ! F4數about Polynomica #5-5-4

1) Let U=a+3, a=U-3

U(U)=5(U-3)-(U-3)^2
=5U-15-U^2+6U-9
= -U^2+11U-24

U(a-1)=U(U-4)
= -(U-4)^2+11(U-4)-24
= -(a-1)^2+11(a-1)-24 <F(U)=F(a)
= -a^2+2a-1+11a-11-24
= -a^2+13a-36

2) Let u=3x x=u/3

T(u)=2(u/3)^2-7(u/3)+2
T(x/2)=2(x/6)^2-7(x/6)+2
=x^2/18-7x/6+2

2014-03-05 23:30:19 補充：
T(u)=2(u/3)^2-7(u/3)+2

2014-03-05 23:30:42 補充：
^ T(u)=T(x)

2014-03-06 00:34:42 補充：
-a^2+13a-36
=(a-4)(9-a)

expand 開就會發現答案一樣了

1)
U(a + 3) = 5a - a²
U(a + 3) = a(5- a)
U(a + 3) = (a + 3 - 3)(8 - a - 3)
U(a + 3) = [(a + 3) - 3][8 - (a + 3)]
U(a - 1) = [(a - 1) - 3][8 - (a - 1)]
U(a - 1) = [a - 1 - 3][8 - a + 1]
U(a - 1) = (a - 4)(9 - a)