Math Help - What is the domain of this function? (I am so confused)

Hello.

I would like to ask what is the domain of the following fucnction.

y=(5x^x)^(x+1)

Our teachers tell us that the domain of a power function (A^X where A is constant and X is a variable) is that the base must be positive and must differ from 1,so in the above example, it is logically that the solution of the following system of inequalities defines the domain:

5x>0 and
5x<>1 and
5x^x>0 and
5x^x<>1


Am I right? And I must note that in our textbook the power function's domain(sorry if I misuse mathematical argo) A^X is that the base A must be positive but it does not say that it must differ from 1. Ohhhh! Please clarify this very obscure situation!

Originally Posted by Val21

Hello.

I would like to ask what is the domain of the following fucnction.

y=(5x^x)^(x+1)

Our teachers tell us that the domain of a power function (A^X where A is constant and X is a variable) is that the base must be positive and must differ from 1,so in the above example, it is logically that the solution of the following system of inequalities defines the domain:

5x>0 and
5x<>1 and
5x^x>0 and
5x^x<>1


Am I right? And I must note that in our textbook the power function's domain(sorry if I misuse mathematical argo) A^X is that the base A must be positive but it does not say that it must differ from 1. Ohhhh! Please clarify this very obscure situation!

Looking at these terms individually, we see that we have no restrictions on the function due to the first factor. The second factor gives us that , since the base must be non-negative, but note that if x = 0 the second factor is , which is undefined. So the domain is x > 0.

-Dan

And what if we take X for 1 so we would get number 1 in the base ,which is prohibited. So probably the domain must be x>0 and x<>1 ?

Thanks for replying

Originally Posted by Val21

And what if we take X for 1 so we would get number 1 in the base ,which is prohibited. So probably the domain must be x>0 and x<>1 ?

Thanks for replying

can also be any integer, so it looks to me as though the domain is:



The union of all positive reals, and non-zero integers.

On second thoughts it looks as though this is also defined when is a rational of
the form (negative rationals which in lowest form have an even numerator)

So my latest bet is:



where .

But somehow I don't think your teacher is looking for an answer of this nature.

RonL

Originally Posted by Val21

And what if we take X for 1 so we would get number 1 in the base ,which is prohibited. So probably the domain must be x>0 and x<>1 ?

Thanks for replying

I don't see why should be prohibited in the base, yes as is undefined, but not .

When , we have:



RonL