What is the name of a function in the form of f(x)^{g(x)}?

[klondike]

I was trying to explain to someone how to find limit of function in form of f(x)^{g(x)} and was asked what kind of function it is. I don't know if this function has a name. Does "power-exponential" sound right?

Thanks!

 

[gopher_p]

Depending on the range of $g$, this expression may or may not make sense if $f$ is ever negative. So without knowing much about $g$ we need to say that $f$ is always strictly positive.

Then $f(x)^{g(x)}=e^{\log f(x)^{g(x)}}=e^{g(x)\log f(x)}$ is really built from elementary functions. I am not aware of this brand of function being given a special name. I suppose you can name it whatever you want.

As long as we're building interesting functions and naming them, what name would you give to $\log_{f(x)}g(x)$?