Question

To have an inverse function, a function f must be ---select--- ; that is, f(a) = f(b) implies a = b

Answer 1

Answer: one-to-one

Another term for this is "injective".

A function is considered one-to-one if each output pairs with a unique input. Visually we can tell if a curve is one-to-one if it passes the horizontal line test. The parabola y = x^2 for instance does not pass the horizontal line test. It doesn't have an inverse function unless we restrict the domain somehow (eg: x ≥ 0)