[tex] f(x) = x^x [/tex](adsbygoogle = window.adsbygoogle || []).push({});

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!

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# [tex] f(x) = x^x [/tex]Given this function, defined, let's say for

**Physics Forums | Science Articles, Homework Help, Discussion**