How to Determine if a Function is One-to-One Algebraically

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In this lesson, we will learn how to determine if a function is one-to-one algebraically. We already learned that a one-to-one function occurs when for each x, there is only one y and for each y, there is only one x. So now we can use this definition to develop a simple test. If f(a) = f(b), this implies that a = b, if the function is one-to-one. So what we can do is plug in an a for x and plug in a b for x and set these two equal to each other. If it turns out that we end up with a = b, then the function is one-to-one.