# What is the domain and range of y = x^x?

Apr 9, 2017

I'd say the domain is $\left(0 , \infty\right)$ because I leave ${0}^{0}$ undefined.
Others allow ${0}^{0} = 1$ so they would give domain $\left[0 , \infty\right)$.
I don't know how to find the range without calculus. The minimum value of ${x}^{x}$ is ${\left(\frac{1}{e}\right)}^{\frac{1}{e}} = {e}^{- \frac{1}{e}} = {e}^{\left(- {e}^{-} 1\right)}$.
Using graphing technology, we can see that the minimum is about $0.6922$