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Domain and range of composite functions?

  1. Apr 4, 2015 #1

    CAH

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    hey!
    How do you work out the domain and range of fg(x), do you work out what range of g(x) will fit the domain of f(x)?

    I have no clue.

    Thanks
     
  2. jcsd
  3. Apr 4, 2015 #2
    Hey CAH,
    Sorry, but do you mean f(g(x)) or f(x) * g(x) ?
     
  4. Apr 4, 2015 #3

    jbriggs444

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    Science Advisor

    °
    Based on the thread title, by fg(x) you mean f(g(x)). So you are trying to work out the domain and range for the composition of f with g.

    For the range, you would start with the range of the inner function -- g in this case. Figure out what outputs are possible from f when its inputs are in that range.

    For the domain, you would start with the domain of the outer function -- f in this case. Figure out what inputs to g can produce outputs in that range.
     
  5. Apr 4, 2015 #4

    CAH

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    for example:
    f(x)=3e^(2x) domain:(-infinity, +infinity)
    g(x)=ln(4x) domain:(0, +infinity)

    how would i go about finding the domain and range of f(g(x))?

    (thanks for the reply)
     
  6. Apr 4, 2015 #5

    HallsofIvy

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    Staff Emeritus
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    First, to be in the domain of f(g(x)), x must first be in the domain of g. Then it must be true that g(x), for that particular x, is in the domain of f. Here, the domain of f is all real numbers so the domain of f(g(x)) is just the domain of g. As for range, g(x) can give any real number but f of any number is positive so the range of f(g(x)) is the set of positive real numbers.
     
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