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: Domain of a composite function

  1. Oct 14, 2014 #1
    1. The problem statement, all variables and given/known data
    Given the Functions
    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


    User Avatar
    Gold Member

    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


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    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


    User Avatar
    Science Advisor

    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 by a moderator: Oct 16, 2014
  6. Oct 15, 2014 #5
    thanks everyone I understand it much better now :D
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted