I am learning about exponential function from math book for high-school.

I have learned about if and . I have understand pretty much of it, but I didn't find any explanation if (why?).

I have tried to understand by myself properties of exponential function if and .

This is what I think are properties:

1) for and function is defined but there is no inverse function

2) for and function is defined but there is inverse function

Can someone explain me a little bit about that?