1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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?
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook