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## Main Question or Discussion Point

[tex] f(x) = x^x [/tex]

Given this function, defined, let's say for all real numbers, is there any way to tell when x is rational versus irrational for integer values of f(x)?

e.g.

[tex] x^x = 4 [/tex]

x = 2

[tex] x^x = 27 [/tex]

x = 3

[tex] x^x = 3 [/tex]

x = 1.825455054...

Thanks!

Given this function, defined, let's say for all real numbers, is there any way to tell when x is rational versus irrational for integer values of f(x)?

e.g.

[tex] x^x = 4 [/tex]

x = 2

[tex] x^x = 27 [/tex]

x = 3

[tex] x^x = 3 [/tex]

x = 1.825455054...

Thanks!

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