(a) Let f : R -> R be defined by f(x) = x^2. Show that f(x) has no inverse function.
(b) Let g : (0,inf) -> R be defined by g(x) = x^2. Show that g(x) has an inverse function.
A function does not have an inverse function when 2 different x values can produce the same y value.
f(-3) = 9
f(3) = 9
So if we were to inverse it, f(9) could be 3 or -3, making it not a function.
Think about why g(x) has an inverese.
Can 2 different x in the domain produce the same y?