# Homework Help: Domain of f(x)^g(x) function

1. Oct 20, 2011

### karkas

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. Oct 20, 2011

### SammyS

Staff Emeritus
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 .