1. Not finding help here? Sign up for a free 30min 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!

Domain of f(x)^g(x) function

  1. Oct 20, 2011 #1
    1. The problem statement, all variables and given/known data
    We have to find the domain range (hope I'm using this right) of some functions, one of them being h(x)=f(x)^g(x), say h(x)=(x^2-4)^(x). I've been looking around and couldn't find the domain range of the x^x function, so I am kinda stuck on this one.


    2. Relevant equations

    Find the domain of h(x)=(x^2 -4)

    3. The attempt at a solution
    Well there's a somewhat obvious requirement (I think), that x^2-4>0 . So we get x>2 or x<-2. Other than that though I don't see any other requirement that stems from the exponent. Maybe that isn't even the case , however. Any suggestions? Thanks!
     
  2. jcsd
  3. Oct 20, 2011 #2

    SammyS

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    xx does pose a problem.

    When x is a negative number, xq, where q is a rational number, is only defined if the numerator of q is even (and it is applied before applying the denominator), or if the denominator of q is odd.

    xr is undefined if r is irrational.

    To my knowledge, the usual practice is to consider the domain of xx to be (0, ∞). While you can make a case for including a subset of the negative rational numbers, to do so puts a lot of holes in the domain for x < 0 .
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook