This is a problem from Discrete Mathematics and its Applications
Book's definition on bijection
Book's definition on onto Book's definition on one to one
I am trying to do problem 23D. Here is my work so far
First I tried showing that the function is a one to one function. I set the equation that if two function outputs of different variables, m, and n have the same output, m and n are actually the same variable. Through some i expression, I got to the equation m^2 = n^2. I wasn't sure how to interpret this. I could have square rooted both sides to get m=n, but at the same time I also thought that if m = -2 and n = 2, they would both evaluate to the same function output, breaking the rule of one to one. Is that the right way to think about it or is m=n if you take the square root of both sides?
Because I was unsure about this, I moved onto to seeing if the function was onto. I know that to do this, you have to solve for the input x to show that yes indeed for every y in the output codomain, there is an x that evaluates to it. How would you do this in this situation? I couldn't find a way to isolate the x because of the squared term and the other term has a y attached to it.