The definition you've provided for a one-to-one function (also called an injective function) needs a slight adjustment for clarity. Here's the correct version:

A function $f(x)$ is one-to-one (or injective) if different values of $x$ map to different values of $y$. More formally:

If $f(x_1) = f(x_2)$, then it must be the case that $x_1 = x_2$.

Alternatively, this means that if $x_1 \neq x_2$, then $f(x_1) \neq f(x_2)$. In simpler terms, no two distinct inputs can have the same output for a function to be one-to-one.

Would you like further examples or explanations?

Here are 5 questions that expand on this information:

1. How do you test if a function is one-to-one using its graph?
2. Can a function be one-to-one but not onto (surjective)?
3. What is an example of a real-world application of injective functions?
4. How does the horizontal line test determine if a function is one-to-one?
5. Can an inverse function exist if the original function is not one-to-one?

Tip: If you can find two different inputs that give the same output, the function is not one-to-one.