Expert: Richard J. Raridon - 3/22/2008

Question
I have 60 question internet assignment that requires you to give the exact answer. I keep on getting theses 8 questions wrong and I tryed them over and over again. Can you please show me how you would do the answer and the work? Thanks


Simplify the following

(x+3)^-1-x^-1
x^2+2x-3/x^2-4* x^2+3x+2/x+3

Solve for X  
2(x+3)^ 4/3-6=26

f(x)=  )square root bracket x+4) , g(x)= suare root bracket x-3

Given the following table of values, determine f(g(h(6)))):  

f(6)=-3 f(3)=1 f(-3)        f(4)=-1
g(6)=2  g(3)=4 g(-3)=2      g(4)=-3
h(6)=3  h(3)=2 h(-3)=-3     h(4)=2

5. Verify algebraically, using composition of functions, that f(x)=1/x+2 and g(x)= 1/x-2  

6 Given the points (1,4) and ( 3,8) on the opposite ends of a diameter of a circle, determin the equation of the circle.

7 a rectanguluar playground is to be fenced off and divided in two by another fence parallel to one side of the playground. Four hundred feet of fencing is to be used. Find the dimensions of the playground that maximize he total enclosed area. What is the maximum area?

*. For the following polynomial functions, use the leading coefficient test to determine the end behavior, find the x- intercepts being sure to state the multiplicity and behavior at each, find the y intercepts, determine alegbrically if the graph has y axis synmetray, orgin symnetry or neither and graph the polynomial

(a)= 6x-x^3-x^5
b g(x)= (x-1)^3(x+2) (x+5)^2  

Answer
1. 1/(x+3) -1/x = (x-x-3)/[x(x+3)] = -3/{x(x+3)]
2. [(x+3)(x-1)]/[(x+2)(x-2)][(x+1)(x+2)]/(x+3) = (x+1)(x-1)/(x-2)
or (x^2-1)/(x-2)
3. 2(x+3)^4/3 = 32, (x+3)^4 = 48, x+3 = +/-2(3^1/4) x =-3 +/-2(3^1/4)
4. You indicate a square root by ^1/2. f(x)=(x+4)^1/2, g(x)=(x-3)^1/2
what are you supposed to do with these?
5. h(6)=3, g(h(6)) = 4, f(g(h(6))) = -1
5. f(x) and g(x) are separate functions.  I don't understand this question
6. center of the circle is at (2,6).  diameter of circle = 2(5^1/2)
so the equation is (x-2)^2 +(y-6)^2 = 5
7. dimensions are 100ft and 66.67ft, area is 6667 ft^2
8. I assume you mean (a) f(x) = 6x-x^3-x^5 = x(3+x^2)(2-x^2)
so the x-intercepts are 0, 2^1/2, -2^1/2, the y-intercept is 0.
You can graph it.  Just put in a value for x, calculate f(x) and plot
(b) Obviously, the x-intercepts are 1,-2,-5