(Section 1.9: Inverses of One-to-One Functions) 1.9.8 In summary … A functionfis invertible±fx()=bhas a uniquesolution, given by x=f±1b, ±b²Rangef±fis one-to-one±The graph of y=in the xy-plane passes the Horizontal Line Test (HLT). • The one-to-one propertyis essential for a function to be invertible, because we need the inverseto be a functionafter inputs are switched with outputs. • (See Footnote 3; we assume the “onto” property.) PART D: GRAPHING INVERSE FUNCTIONSBy the “Input-Output” Properties, a,b±f²b,a±f³1. Graphical Properties of Inverse Functions
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