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Composition of functions and being defined thru range and domain

  1. Aug 13, 2009 #1
    For the following to be defined doesn't
    1) range(f) ⊆ domain(g)
    2) range(g) ⊆ domain(h)

    Is that correct? So R ⊆ R for 1, and R ⊆ R for the other so it is ok?
    Second question: but 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?????
    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

    Find composition h o g o f and simplify.


    h(g(f(x)) = e^3lnx = x^3 , defined for all real numbers (??)
    Last edited: Aug 13, 2009
  2. jcsd
  3. Aug 13, 2009 #2


    Staff: Mentor

    Do not post the same problem in two different forums. You posted this problem in the Calculus and Above forum, but with a different answer.

    Your answer here is partly correct. When are e3 lnx and x3 equal?
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