Precalc0108to0109-page18

Precalc0108to0109-page18 - (Section 1.9: Inverses of...

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(Section 1.9: Inverses of One-to-One Functions) 1.9.8 In summary … A function f is invertible ± fx () = b has a unique solution, given by x = f ± 1 b , ± b ² Range f ± f is one-to-one ± The graph of y = in the xy -plane passes the Horizontal Line Test (HLT) . • The one-to-one property is essential for a function to be invertible , because we need the inverse to be a function after inputs are switched with outputs. • (See Footnote 3; we assume the “onto” property.) PART D: GRAPHING INVERSE FUNCTIONS By the “Input-Output” Properties, a , b ± f ² b , a ± f ³ 1 . Graphical Properties of Inverse Functions
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