Question 0.3.2: A Function with No Inverse Show that f (x) = x² has no inver...

Notice that f (4) = 16 and f (−4) = 16. That is, there are two x-values that produce the same y-value. So, if we were to try to define an inverse of f, how would we define f^{-1}(16)? Look at the graph of y=x^2 (see Figure 0.40) to see what the problem is. For each y > 0, there are two x-values for which y=x^2. Because of this, the function does not have an inverse.