College Algebra / Unit 7 Alg 388 short lesson, about 20 seconds
Restricting a Domain for an Inverse
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The idea
A function that fails one-to-one earns an inverse by domain restriction: keep a piece where no output repeats, invert the piece.
In practice
f(x) = x² fails the horizontal line test — but restricted to [0, ∞) it passes, and its inverse is √x: f⁻¹(9) = 3, the nonnegative root.
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