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

1 Answer
Jim H
Apr 9, 2017

I'd say the domain is #(0,oo)# because I leave #0^0# undefined.
Others allow #0^0=1# so they would give domain #[0,oo)#.

Explanation:

Range.

I don't know how to find the range without calculus. The minimum value of #x^x# is #(1/e)^(1/e) = e^(-1/e) = e^((-e^-1))#.

Using graphing technology, we can see that the minimum is about #0.6922#

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