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Finding domain and ranges for composition function

  1. Dec 14, 2013 #1
    1. The problem statement, all variables and given/known data

    Find the domain and range of (f+g)(x)
    Given that
    F(x)= 1/(x-1) and g(x) = sqrt(x)



    2. Relevant equations



    3. The attempt at a solution
    I added the two functions to get 1/(x-1) + sqrt(x)

    To get domain, i look at the restrictive x values for both to get x greater than 0 and not equal to 1.
    However how do i find the range?
     
    Last edited: Dec 14, 2013
  2. jcsd
  3. Dec 14, 2013 #2

    Mark44

    Staff: Mentor

    Graph both functions separately, preferably using different colors for each graph. Then, using a third color, or a marker pen, go over the parts of the two graphs for which x ≥ 0 and x ≠ 1. From that graph it should be evident what the range of the sum function is.
    The graph of the product function is a parabola that opens downward. You should already have a technique for finding the vertex of a parabola. Let's say that the vertex is at (a, b). Then the range will be {y| -∞ < y ≤ b}.

    BTW, you misposted this problem in one of the physics sections. This is a precalc type problem, so I moved it to this section.
     
  4. Dec 14, 2013 #3
    is there another way to find the range without graphing it?
    the answer is y less than -0.7886 or y greater than 2.2287.
    How can you get to that precise of an answer when graphing it by hand??
     
  5. Dec 14, 2013 #4

    Mark44

    Staff: Mentor

    They're probably using a graphing calculator or some graphing utility.
     
  6. Dec 15, 2013 #5
    ImageUploadedByPhysics Forums1387135472.474199.jpg
    For the second graph (f+g)(x)
    The range in the back of the book says y less than .75 but u can see clearly in the graph that it is less than 1 ... What is going on?
     
  7. Dec 15, 2013 #6

    ImageUploadedByPhysics Forums1387136498.132607.jpg
    I drew the graph out it is just a sketch and would not be accurate on the range.. Are you expected to know precisely where it is?
     
  8. Dec 15, 2013 #7

    Mark44

    Staff: Mentor

    The graphs don't show the sum or difference of the two functions. Those (sum or difference) are the graphs of interest here.
     
  9. Dec 15, 2013 #8
    The thing is how do you graph 1/(x-1) + sqrt (x)?
     
  10. Dec 15, 2013 #9

    Mark44

    Staff: Mentor

    You can get a rough graph by doing it by hand. Pick values of x there are in the common domain for both functions (x ≥ 0, and x ≠ 1), the calculate the y-values.

    As I said before, they are probably using a graphing calculator or computer graphics package.
     
  11. Dec 15, 2013 #10
    So for example I would take 0.5 and plug it into the composite formula?
     
  12. Dec 15, 2013 #11
    But the range won't be accurate right?
     
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