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Domain of a composite function

  1. Oct 14, 2014 #1
    1. The problem statement, all variables and given/known data
    Given the Functions
    f(x)=4x-1
    g(x)=3-2x^2
    h(x)= sqrt (x+5)

    What is the domain of h(g(x))?
    2. Relevant equations

    the subject is finding the domain of a composite function
    3. The attempt at a solution
    I don't understand what I have to 'bring over' from g(x). I think x cannot equal zero for g(x). If someone could post a structured list of steps I need to take to find the domain of a composite function, it would be much appreciated.

    thank you
     
  2. jcsd
  3. Oct 15, 2014 #2

    ShayanJ

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    The domain of a composite function [itex] (f \circ g)(x)=f(g(x)) [/itex] is defined as [itex] D(f\circ g)=\{x \epsilon D(g) | g(x) \epsilon D(f) \} [/itex]. So you should find the domains of f and g and check that for what subset of the domain of g, it gives values in the domain of f.
     
  4. Oct 15, 2014 #3

    LCKurtz

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    Why do you think that? ##g(x)## is just a polynomial. What' wrong with ##g(0)##?
    What is the formula for ##h(g(x))##? What values of ##x## work in that?
     
  5. Oct 15, 2014 #4

    HallsofIvy

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    The domain of square root is "numbers greater than or equal to 0". h(x)= sqrt(x- 5) so the domain of h is "[itex]x- 5\ge 0[/itex] or [itex]x\ge 5[/itex]. That means that [itex]g(x)= 3- 2x^2[/itex] must give only values greater than or equal to 5. Can you solve [itex]3- 2x^2\ge 5[/itex]?
     
    Last edited: Oct 16, 2014
  6. Oct 15, 2014 #5
    thanks everyone I understand it much better now :D
     
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