ACT OF UNION BETWEEN THE EASTERN AND WESTERN CHEROKEES. WHEREAS, our fathers have existed as a separate and distinct Nation, in the possession and exercise of the essential and appropriate attributes of sovereignty, from a period extending into antiquity, beyond the records and memory of man; and
A surjective function f from the real numbers to the real numbers possesses an inverse as long as it is one-to-one, i.e. as long as the graph of y = f(x) has, for each possible y value only one corresponding x value, and thus passes the horizontal line test.
If you think of functions with exponents, you're probably used to seeing something like this. That's the graph of y = x^2, and it is indeed a function with an exponent. But it's not an exponential function. In an exponential function, the independent variable, or x-value, is the exponent, while the base is a constant. For example, y = 2^x would be an exponential function. Here's what that looks like.