Question

数学问题！难死我了！高手帮帮忙！

请高手来帮我解答下~分没多少！ 谢谢了 （我和洋人比拼啊 不能输啊同志们）！
请把解题过程写出来 谢谢！

1. Let f(x)=(2X^2 - 2)/(X^2 -3X-40)
a. Factor the umerator and denominator. Determine where each factor is zero.
b. Determine the X- intercepts, Y-intercept, Vertical asymptotes, and horizontal asymptote.
c. Solve (2x^2 -2)/(x^2 -3X-40) > 2

2. Let f(x)=(X+1)/(3X-5)
a. What is the domain and range of f(x)?
b. Compute the inverse of f(x). What is the domain and range of the inverse function?
3. Let f(x)= - (根号x-3)+1
a. what is the doain and range of f(x)?
b.Compute the inverse of f(x). What is the domain and range of the inverse

4. Suppose you invest $12,000 into ana account earning 3% interest.

a. Determine a formula B(t) for the balance of the account( where t is years since the account was opened)provided the interest is COMPOUNDED 4 TIMES A YEAR. What is the balance of the account after 10 years? About how long will it take the account to double in value?
b.Determine a formula B(t) for the balance of the account( where t is years since the account was opened)provided the interest is COMPOUNDED 12 TIMES A YEAR. What is the balance of the account after 10 years? About how long will it take the account to double in value?

Answer 1

1、
a.Factor (2x²- 2)=2(x-1)(x+1)，(x²-3x-40)＝(x-8)(x+5)；
When x=1 or -1，numerator is zero；When x=8 or -5，denominator is zero；
b. The x- intercepts：8 and -5；y-intercept：2；
Vertical asymptotes：x=8 and x=-5；horizontal asymptote：y=f(x)=2；
c. (2x²-2)/(x²-3x-40) > 2；
The detailed process as follows：
If x>8 or x<-5，the inequation degenerate into (2x²-2)>2(x²-3x-40)，that is x>-13；
Thus x>8 or -13<x<-5 can satisfied the inequation;
If -5<x<8，the inequation degenerate into (2x²-2)<2(x²-3x-40),that require x<-13,no solution；
2、f(x)=(x+1)/(3x-5)，the domain x∈R,x≠5/3；Range of f(x)：(-∝,1/3)、(1/3,+∝)；
inverse function f(y)=(1-5y)/(3y-1)；the domain y∈R,y≠1/3；Range of f(y)：(-∝,5/3)、(5/3,+∝)；
3、f(x)= - √(x-3)+1,the domain x≧3；range of f(x)=(-∝,1]；
inverse function f(y)=(1-y)²+3;,the domain x∈R,range of f(y)=[3,+∝)；
4、
a. B(t)=12000(1+0.75%)^(4t)；
B(10)=12000(1+0.75%)^(4*10)=12000*1.3483=16180.18；
When the account double in value B(t)=24000，(1+0.75%)^(4t)=2，
We can achieve： t=(lg2/lg1.0075)/4=23.19(years)≈23；
b. B(t)=12000(1+0.25%)^(12t)；
B(10)=12000(1+0.25%)^(12*10)=12000*1.3494=16192.24；
t=(lg2/lg1.0025)/12=23.13(years)≈23；

Answer 2

【额，你貌似打错了点什么。。。你最好check一下】【另外，其实题很简单啊。。。】

追问

没有错的！

追答

不是数字的错误，是貌似有英文打错了，我不知道你那句话什么意思

Answer 3

你跟洋人比拼的题不是中文版的那么

Answer 4

我草拿自己的本事比去