Domain of a function

Discussion in 'Calculus' started by marco.marsella, Jun 24, 2021.

1. marco.marsella

Joined:
Jun 24, 2021
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The domain of the function:

(1) f(x) = x^x

is known to be [0 .. inf).
Considering that x = 2x/2, it is possible to rewrite the function as:

(2) f(x) = x^(2x/2)

Using the multiplicative property of the exponentials it is possible to rewrite it again as:

(3) f(x) = (x^2)^(x/2)

The function (3) is now defined over the whole real axis, as x^2 > 0, for all x.
The online plotting tools agree with this and draw the functions (1) and (3) on two different domains.
Since a function cannot have two domains, I suppose I wrote something wrong and the two functions (1) and (3) are indeed different.
Unfortunately, I can't find what's wrong... the mathematics seems easy...

Thanks for helping and regards,
Marco

marco.marsella, Jun 24, 2021

Joined:
Jun 27, 2021
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