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Homework Help: Function questions

  1. Apr 17, 2007 #1
    1. The problem statement, all variables and given/known data
    a) If f and g are continous functions how do you show f-g is continous?

    b) if f is continous then f inverse exists?


    3. The attempt at a solution
    a) Do you look at the sets that f and g maps points in the domain into?

    b) I think so.
     
  2. jcsd
  3. Apr 17, 2007 #2

    HallsofIvy

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    (a) How about looking at [itex]|f(x)- g(x)- (f(a)- g(a))|\le |f(x)- f(a)|+ |g(x)-g(a)| as just about every calculus book does? Since f is continuous (at a) you can make that first absolute value less than any [itex]\epsilon[/itex], since g is continuous (at a), you can make the second absolute value less than any epsilon.

    (b) What about y= x2 with domain all real numbers? Is it continous? Does it have an inverse? What do the DEFINITIONS of "continous" and "inverse function" have to do with each other?
     
  4. Apr 17, 2007 #3
    For y=x^2 it has an inverse for [0,infinity) but not all the real numbers, so no for b)
     
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