There is attached file with my input.The wolfram gave the x=2 as solution but is supposed to be out of the domain because when x=2 the base of the exponential function equal to 0.
I will be happy for clarification if im wrong
You don't need exponential, just elementary powers: 0^2=0*0, 0^3=0*0*0 and so on.
0^2=0*0
0^3=0*0*0
But in fact i do have 2 exponential , and that give me a domain
Try this:
In[1]:= FunctionDomain[x^y,{x,y}] Out[1]= (y \[Element] Integers && x != 0) || (y \[Element] Integers && y >= 1) || (x >= 0 && y > 0) || x > 0
When the exponent is a positive integer, there is no restriction at all on the base.
So if i understood comoletly. The base can never be an negative And the base can be 0 if is sure that the exponent is positive?
The base can be negative if the exponent is integer. For example (-1)^3.
(-1)^3
You can do negative numbers raised to a noninteger power if you are comfortable with multivalued complex results. In those cases the usual algebraic rules of powers break down and you must be very careful. I is an endless source of confusion and it turns up regularly on this list.
I see no problem with zero raised to a positive integer, like 0^4 or 0^5.
0^4
0^5
But there isn't domain in exponential function that the base need to be bigger than 0?
