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How to find the correct domain for a composite function?

  1. Feb 8, 2017 #1
    1. The problem statement, all variables and given/known data
    The problem states f(x)= √x-5). When solving for (f)/(f)(x) I got the answer=√(√x-5)
    I cannot get the interval notation correct as many times as I input the domain. The square root must of a square root has confused me.

    2. Relevant equations
    Please view the attached screen shot Screenshot 2017-02-07 at 9.55.33 PM.png

    3. The attempt at a solution
  2. jcsd
  3. Feb 26, 2018 #2


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    The square root is more restrictive, do you see why? What is the domain of h(a) = √a ? (what values of a are valid?)
    Now what if a = x-5, what are the values that x can be for it to be valid? That is the way that I think about it.

    Now try a = x2-5.
  4. Feb 26, 2018 #3


    Staff: Mentor

    According to your work in the screen shot, ##f(x) = \sqrt{x - 5}##.
    You should have written f(x) = √(x - 5). It looks like you sort of intended to do this, but omitted the left parenthesis.
  5. Mar 2, 2018 #4
    OK, so [tex]f(x):=x^2[/tex] and [tex]g(x):=\sqrt{x-5}[/tex]

    You must undertand that [tex]x\in Dom(f\circ g)[/tex] iff [tex]x\in Dom(g)[/tex] and [tex]g(x)\in Dom(f)[/tex]

    Obviously [tex]Dom(f)=\mathbb{R}[/tex], and [tex]Dom(g)=[5,+\inf)[/tex]

    So what is [tex]Dom(f\circ g)[/tex] ?
  6. Mar 2, 2018 #5
    It is f ∘ g.
    so basicly, f(g(x)).
    So cuz f(x)=x^2, f(g(x))=(g(x)^2.
  7. Mar 2, 2018 #6


    Staff: Mentor

    No it doesn't, at least if we are to believe your screen shot. In that image, it clearly shows that ##f(x) = x^2##.
    This notation makes no sense. The problem asks for f(f(x)), among other things.
  8. Mar 2, 2018 #7


    Staff: Mentor

    Thread closed. For some reason, the OP is not a member here, so won't be able to reply.
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