Calculate domain $f(x)=x^{\frac{x+1}{x+2}}$ I have the following function:
$$f(x)=x^{\frac{x+1}{x+2}}$$
I tried to calculate the domain, which seems easy, and my result is: $D(f)=(0,\infty)$.
When I tried to calculate it, by using Wolfram-Alpha, I obtain: $D(f)=[0,\infty)$.
Can someone explain me the reason, or if it is just a Wolfram's error?

I proceed in this way:
$$f(x)=x^{\frac{x+1}{x+2}} = e^{\frac{x+1}{x+2} \log(x)}$$
$$
\left\{ 
\begin{array}{c}
x+2\ne0 \ \Rightarrow\ x\ne -2 \\ 
x>0
\end{array}
\right. 
$$
Hence: $D(f)=(0,\infty)$.

The domain and range functionality in WolframAlpha was designed specifically to answer questions for students in algebra, precalculus, and calculus. In that context, the convention that $0^{1/2}=0$ is quite reasonable. As you might hope, it's also completely consistent with the way that Mathematica treats things. For example:
In[1]:= Log[0]
Out[1]= -Infinity

In[2]:= Exp[-Infinity]
Out[2]= 0

Now, as others have argued, there are other reasonable ways to interpret $0^{1/2}$ and that's fine. If your objective is to understand WolframAlpha's response, however, then it's a simple matter of design choice.
