One-to-One Functions & Inverse Function PDF
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This document explains one-to-one functions and inverse functions in mathematics. It uses diagrams and examples to illustrate the concepts and includes a horizontal line test. The document appears to be a lecture or handout, rather than an exam.
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One-to-One Functions; Inverse Function A function f is one-to-one if for each x in the domain of f there is exactly one y in the range and no y in the range is the image of more than one x in the domain. A function is not one-to-one if two different elements in the domain correspond to the same...
One-to-One Functions; Inverse Function A function f is one-to-one if for each x in the domain of f there is exactly one y in the range and no y in the range is the image of more than one x in the domain. A function is not one-to-one if two different elements in the domain correspond to the same element in the range. x₁ y₁ x₁ y₁ x₂ y₂ x₂ x₃ x₃ y₃ Domai Rang y₃ n e Domai One-to-one Rang n e function NOT One-to-one function x₁ y₁ y₂ x₃ y₃ Not a Domai Rang function n e M: Mother Function is NOT one-one Joe Samanth Laura a Julie Anna Hilary Ian Barbara Chelsea Sue George Mothers S: Social Security function IS one- one Joe 12345678 Samanth 9 a 22345678 Anna 9 Ian 33345678 Chelsea 9 George 43345678 9 53345678 9 63345678 9 SSN Is the function f below one – one? 1 10 2 11 3 12 4 13 5 14 6 15 7 16 Theorem Horizontal Line Test If horizontal lines intersect the graph of a function f in at most one point, then f is one-to-one. Use the graph to determine whether the function is one-to-one. Not one-to-one. Use the graph to determine whether the function is one-to- one. One-to-one. Which of the following is a one-one functions? 1. The relation pairing an SSS member to his or her SSS number 2. The relation pairing a real number to its square 3. The relation pairing a person to his or her citizenship
