Inverse Functions (recognizing)

WE know how to graph four types of unctions including y=x, y=root of x, y=x^2, and y=1/x . However, we only had one lesson on INVERSE functions and then this homework which, in several questions, asks us to dtermine whether the inverse of a function is a function (poor wording on the book's behalf). The way we learned in determining this stuff is that, doing a vertical line test on a function proves it is a function, and doing a horizontal line test on an inverse function proves it is an inverse function. At the same time, we know the definition of a function to be "a rule that provides a single input for every valid input" and an inverse function... But what we can't quite do yet is recognize (simply based on the equation) is the inverse of a function is "a function" ... Now, like I said, the book gives poor wording so I don't quite understand what it means when it says to "find the inverse of a function and determine whether it is a function" , so perhaps who ever is reading htis can decide for themselves, but I am looking for an easier way to dterming whether an equation that the book gives IS an inverse function, or whether an equation the book gives IS a Function.... Simply by looking at the equation hopefully