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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).

Definition 9. Let f be a one-to-one function. The inverse of f, denoted by f−1, is the unique function with domain equal to the range of f that satisfies f f−1(x) = x for all x in the range of f. Warning DON’T Confuse f−1 with the reciprocal of f, that is, with 1/f. The “−1”

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