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Lecture 1 - UH

Lecture 1 Section One-To-One Functions; InversesJiwen He1 One-To-One Definition of the One-To-One FunctionsWhat are One-To-One Functions? Geometric TestHorizontal Line Test If some horizontal line intersects the graph of the function more than once,then the function is not one-to-one. If no horizontal line intersects the graph of the function more than once,then the function is are One-To-One Functions? algebraic TestDefinition functionfis said to beone-to-one(or injective) iff(x1) =f(x2) impliesx1= functionfis one-to-one if and only if x1, x2,x16=x2impliesf(x1)6=f(x2).

Algebraic Test Definition 1. A function f is said to be one-to-one (or injective) if f(x 1) = f(x 2) implies x 1 = x 2. Lemma 2. The function f is one-to-one if and only if ∀x ... The graph of f−1 is the graph of f reflected in the line y = x. Example 13. Given the graph of …

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