[F4 Maths] Functions

由 leungfan » 2010年11月9日 22:35:11 (p#2004240)

29. It is given that g(x)=2x-1.
(a) If h(x)=g(2x-1), find the algebraic representation of h(x).
g(2x-1)=2(2x-1)-1=h(x)
h(x)=4x-3
(b) If g(p-2)=h(p), find the value of p

31. The graph of y=(k-1)x+2k, where k>1. It cuts x-axis & y-axis at A&B respectively. If area of AOB = 9 sq. units, find all possible values of k
　　　　　 y
　　　　　 ^
　　　　　 B

A　　　　　O --> x
AB= Graph of y=(k-1)x+2k
OA= Length of A
OB= Leugth of B

37. Let f(x)=-x^2+10x+5. p and q are 2 unequal real numbers such that f(p) = f(q). Find value of (p+q)/2

38. 題略
(a) Express y in terms of x.
y=11-x
(b) Express A as a function of x State the domain of functions
A=-x^2+12x+3 **未做後半部分..

40. ABC is an isosceles triangle, where AB=8 cm and AC=BC=5cm. A rectangle PQRS is inscribed in ABC and SC=RC. Suppose SF= x cm
(a) Show that the area of PQRS is {3x-[(3/8)x^2]}cm^2
(b) Find the area of largest rectangle that can be inscribed in ABC

*藍字為本人計算之answer(正確) :D
粗體為圖解

thx a lot... [呢課搞到我頭都大埋...根本唔明佢up乜... 明左前面唔明後面 , 到明左後面果半課就變左唔記得前面果d講乜... 到quiz / revision就 mix哂d野一齊>3<]

由 loklok » 2010年11月9日 23:09:39 (p#2004265)

tridentenviro :29. It is given that g(x)=2x-1.

(a) If h(x)=g(2x-1), find the algebraic representation of h(x).
g(2x-1)=2(2x-1)-1=h(x)
h(x)=4x-3

(b) If g(p-2)=h(p), find the value of p

(b) 將個 h(x) 入面的 x 代返做 p 而已

h(p) = 4p-3
g(p-2) = 2(p-2)-1 = 2p-5

h(p) = g(p-2)
4p-3 = 2p-5
p = -1

由 leungfan » 2010年11月10日 08:25:06 (p#2004349)

GJFT :
tridentenviro :29. It is given that g(x)=2x-1.

(a) If h(x)=g(2x-1), find the algebraic representation of h(x).
g(2x-1)=2(2x-1)-1=h(x)
h(x)=4x-3

(b) If g(p-2)=h(p), find the value of p

(b) 將個 h(x) 入面的 x 代返做 p 而已

h(p) = 4p-3
g(p-2) = 2(p-2)-1 = 2p-5

h(p) = g(p-2)
4p-3 = 2p-5
p = -1

即係part b 只係需要計到g(p-2), 唔洗計h(p)??

由 brianlhm » 2010年11月10日 17:58:42 (p#2004455)

31.x-intercept=-2K/(k-1)
y-intercepy=2K
area=abs(-2k/(k-1))x2k/2=9 (since area>0, get a positive x)
k=3 or 1.5

37
f(p)=f(q)
f(p)-f(q)=0
-P^2+10P+5=-q^2+10q+5
(p^2-q^2)+10(q-p)=0
(p+q)(p-q)-10(p-q)=0
p+q=10
(p+q)/2=5

40. I think SR= x cm instead of SF
let CD be a straight line which is perpendicular to AB
triangle CRS similar to triangle CAB(AAA)
CD^2=(AC^2-AB^2)^0.5 (pyth.theorem)
CD=3
(3-RQ)/3=x=8
RQ = 3-(3/8) x
area= 3x-(3/8)x^2

b)有冇學differentiation?有就用