This was a question on a recent Term Test. I was not sure how to prove the second part of the question and my professor never shows the answers, even after the fact. If someone could please show me how it is solved. I never know how to approach the INT function.
This is how I answered it, but like I said, I am really not sure: the range of f is (-∞,∞). To find the inverse, we need to consider 2 cases in which x is an integer and x is not an integer: When x is a integer, f(x)=2x so its inverse becomes g(x)=x/2 When x is not an integer the function f becomes f(x)=x+[x]. So there is no inverse for the function when it is not an integer since it cannot form a relation. So f^-1(x)=2x ;x is an integer.