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Unit 30 Functions

Unit 30 Functions. Unit 30. 30.1 Functions, Mappings and Domains 1. Example If , use the mapping diagram below to show how v maps to p for . Consider integer values of v. Solution. Extension Question What is the range for p ? Is this 1:1 mapping? Yes. ?. ?. v

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Unit 30 Functions

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  1. Unit 30Functions

  2. Unit 30 30.1 Functions, Mappings and Domains 1

  3. Example If , use the mapping diagram below to show how v maps to p for . Consider integer values of v. Solution Extension Question What is the range for p? Is this 1:1 mapping? Yes ? ? v (domain for p) p

  4. Unit 30 30.2 Functions, Mapping and Domains 2

  5. Example Complete the mapping diagram below for the function Consider integer values of x. Solution Extension Questions What is the range for y? Is this 1:1 mapping? No ? ?

  6. Unit 30 30.3 Functions, Mappings and Domains 3

  7. Example If f is defined by; for all ,what are the values of: (a) (b) (c) (d) Extension Question What is the range of f ? Sketch the function; Solution (a) (b) (c) (d) ? ? ? ? ? ? ? y ? ? ? ? ? ? x -1 1 2 -2 The function f is not a 1:1 mapping. Explain why not? all map to 0 ?

  8. Unit 30 30.4 Composite Functions

  9. The concept of a function of a function is introduced here. • Example • The functions of f and g are defined by • Find and • What are the values of and • Solution • (a) (b) ? ? ? ? ? ? ? ? ? ? ? ? ? ?

  10. Unit 30 30.5 Inverse Functions 1

  11. If , we can make C the subject of the equation by writing or We say that F and C are inversefunctions. For inverse functions, f and g, then Example Show that if then Solution ? ? ? ? ? Note: We write or to mean ,etc.

  12. Unit 30 30.6 Inverse Function 2

  13. For functions that are 1:1 mappings, we can find their inverse functions. Example If , find it’s inverse function. Solution Let and find x as a function of y. i.e. Check ? ? ? ? ? ? ? ? ? ? ? ?

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