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Discuss continuity of the composite function

  1. Feb 27, 2009 #1
    1. The problem statement, all variables and given/known data :
    discuss continuity of the composite function h(x)=f(g(x)) when A} F(x)=X^2 , g(x) = x-1
    B} f(x) = 1/x-6 , g(x) = X^2+5
    where should I start ?
     
  2. jcsd
  3. Feb 27, 2009 #2
    Re: continuity

    h is continuous at a point a if f is continuous at g(a)
     
  4. Feb 27, 2009 #3
    Re: continuity

    and how can we find out what a is if we are not given a number for a ?
     
  5. Feb 27, 2009 #4

    HallsofIvy

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    Re: continuity

    Consider all numbers! At what values of x is f(x)= 1/(x- 6) NOT continuous? (That's the crucial question.)
     
  6. Feb 27, 2009 #5
    Re: continuity

    when x = -6, that would make f(x) = 1/x-6 discontinuous right?
     
  7. Feb 27, 2009 #6

    HallsofIvy

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    Re: continuity

    Please use parentheses.
    If you mean f(x)= (1/x)- 6, then f(-6)= -1/6- 6= -37/6. No this function is not discontinuous at -6.

    If you mean f(x)= 1/(x- 6), then f(-6)= 1/(-6-6)= -1/12. No this function is not discontinuous at -6.

    Be more careful!
     
  8. Feb 27, 2009 #7
    Re: continuity

    f(6) = 1/ (6-6) = 1/0 this function is discontinuous, right ?
     
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