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Composition of functions, domain, range

  1. Aug 13, 2009 #1
    A = (0, infinity), B = C = D = R where R is all real numbers
    f: A->B, g: B->C, h: C->D
    f(x) = lnx, g(y) = 3y, h(z) = e^z
    h o g o f ?

    For the following to be defined doesn't
    1) range(f) ⊆ domain(g)
    2) range(g o f) ⊆ domain(h)

    So g o f should be defined since R ⊆ R and h o (g o f) should be defined since R ⊆ R.

    But I don't understand how can you have the function h with the range of all real numbers when the exponential function only has a range of all positive real numbers?????

    So, what will the domain of the result be?

    h(g(f(x)) = x^2 , all reals (?)
    Last edited: Aug 13, 2009
  2. jcsd
  3. Aug 13, 2009 #2


    Staff: Mentor

    Your formula h(g(f(x))) is incorrect. Work it out again without simplifying it.
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