Math question for a final tomorrow?

Question

Okay, so I have a final in math tomorrow; I feel comfortable with everything else covered, but these type of problems I have issues and difficulty solving, and am asking , not for an answer but, how to get through the problem; preferebly just an explanation on how to go about them; My Professor is being incredibly generous and saying that, if, on our final we make a grade that is higher than our current average, mine being a 67.84 (no rounding :&#92;), he will replace all lower grades with the score that you receive on the final.

These questions are from previous exams, and are the ones that I truly cannot figure out without explanation, and need a clearer explanation, and basically a walk through.

1. Find the Inverse of the function: f(x) = 2 ln (3x+5).

2. Find the domain of the composition named below without first finding the rule for the composition. If f(x)=x/x-3;g(x)=x-1/2x+4, find the domain of FoG. Sketch the solution on the real number line. Express answer in Interval Notation. (This one confuses me, because there are two boxes with arrows, so it's like... <-[]<- blank spot <-[]<-; and that I have no clue how to do the line, because it's...The best I can guess is putting it at f(g(x)), but not how to put it in the box.)

3. Answer questions with the following function: f(x) = x+1/3x-1.
      c.) If f(x)= 3, what is x? What is the corresponding point on the graph?
      d.) List x-intercepts, if any, of the graph of f?
      e.) List the y-intercepts, if any, of the graph of f?


Those are the types of problems that I just cannot figure out properly. It'd be really nice, if someone could help out a bit :3

Note: I have a feeling that there are going to be some replies regarding not paying attention, but then there'd be no point in having Yahoo Answers if you can't ask questions, now is there? Personally, I don't care about answers, but more how to DO them.

Tugsuu · Accepted Answer

1. Let's substitute x for y and y for x so that x = 2 ln (3y + 5). 
a) x/2 = ln (3y + 5)
b) e^(x/2) = 3y + 5
c) e^(x/2) - 5 = 3y
d) (e^(x/2) - 5)/3 = y

2. Domain of f(x): (-inf, 3) U (3, inf)
    Domain of g(x): (-inf, -2) U (-2, inf)
    3 = g(x) = (x - 1)(2x + 4)
    6x + 12 = x - 1
    5x = -13
    x = -13/5
    x cannot equal -13/5 because then g(x) would be 3 which is not in the domain of f(x)
    Domain: (-inf, -13/5) U (-13/5, -2) U (-2, inf)

3. c) f(x) = 3 = (x+1)/(3x - 1)
       3(3x - 1) = x + 1
       9x - 3 = x + 1
       8x = 4
       x = 1/2
   d) 0 = (x + 1)/(3x - 1)
       x + 1 = 0
      x = -1
      (-1, 0)
  e) ((0) + 1)/(3(0) - 1)
      (1)/(-1)
      -1
      (0, -1)

Blake · Answer

1) To find the inverse of y = 2 ln(3x+5), all you gotta do is switch x and y. After that, you'll need to divide by 2 and rewrite the equation into exponential form. Don't forget your base is e because of the ln().
2) I'm not quite sure about this one, but my best guess is rewriting f(g(x)) and then setting the denominator (bottom part) = 0 and solving. When you find x, your domain should be all real numbers except what you had x equal because you can't divide by 0.
3) c) Plug in 3 for f(x) and solve. Your first step is to multiply by 3x - 1 on each side.
d) Plug in 0 for f(x) and solve. This is because an x intercept is where y = 0.
e) Plug in 0 for x and solve. This is because a y intercept is where x = 0.

Hope this helped!

? · Answer

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Math question for a final tomorrow?

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