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Presentation transcript:

Inverse functions Mathematics Department University of Leicester

Content How to find an inverseExamplesIntroduction

Next How to find an Inverse Examples If a function applies an action to a set then it is useful to know how to undo that action. The inverse function is the “undoing” function. If we know how to convert a temperature from Fahrenheit to Celsius, can we work out how to convert from Celsius to Fahrenheit? This would require calculating inverses! Introduction

Inverse functions Next How to find an Inverse ExamplesIntroduction

Next How to find an Inverse ExamplesIntroduction

Your turn None of these How to find an Inverse ExamplesIntroduction

Your turn None of these How to find an Inverse ExamplesIntroduction

Domain & Range Range Domain Range Domain Next How to find an Inverse ExamplesIntroduction

Example question Solution How to find an Inverse ExamplesIntroduction

Example question Next How to find an Inverse ExamplesIntroduction

Graphs of inverses Next How to find an Inverse ExamplesIntroduction

Next How to find an Inverse Examples Introduction

Investigating inverses Sine inverse Cosine inverse Exp inverse Log inverse y x y = x How to find an Inverse Examples Next Introduction

x Sine inverse Cosine inverse Exp inverse Log inverse Investigating inverses yy = x Next How to find an Inverse ExamplesIntroduction

x Sine inverse Cosine inverse Exp inverse Log inverse Investigating inverses yy = x Next How to find an Inverse ExamplesIntroduction

x Sine inverse Cosine inverse Exp inverse Log inverse Investigating inverses yy = x Next How to find an Inverse ExamplesIntroduction

x Sine inverse Cosine inverse Exp inverse Log inverse Investigating inverses yy = x Next How to find an Inverse ExamplesIntroduction

x Sine inverse Cosine inverse Exp inverse Log inverse Investigating inverses yy = x Next How to find an Inverse ExamplesIntroduction

x Sine inverse Cosine inverse Exp inverse Log inverse Investigating inverses yy = x Next How to find an Inverse ExamplesIntroduction

x Sine inverse Cosine inverse Exp inverse Log inverse Investigating inverses yy = x Next How to find an Inverse ExamplesIntroduction

x Sine inverse Cosine inverse Exp inverse Log inverse Investigating inverses yy = x Next How to find an Inverse ExamplesIntroduction

x Sine inverse Cosine inverse Exp inverse Log inverse Investigating inverses Next How to find an Inverse ExamplesIntroduction

Question How to find an Inverse ExamplesIntroduction

Conclusion Next How to find an Inverse Examples You should now be able to: Calculate inverses. Calculate the range and domain of an inverse. Draw the graph of an inverse function. Introduction