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[FUNCTIONS] Composite Functions + Inverse Functions JC MATHS SITCOMS

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[FUNCTIONS] Composite Functions + Inverse Functions

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Overview

How do we find composite functions and determine whether they exist?

2. [FUNCTIONS] Composite Functions

What happens when there is a piecewise function?

3. [FUNCTIONS] Composite Functions

What is the condition for composite functions? Are you able to identify correctly?

4. [FUNCTIONS] Composite Functions

What happens when you map a function to itself?

5. [FUNCTIONS] Inverse Functions

How do we find inverse functions? What are the conditions for inverse functions to exist?

6. [FUNCTIONS] Inverse Functions

What are the conditions for an inverse function to exist? How do we find the inverse function?

7. [FUNCTIONS] Inverse Functions

Condition & Rule

8. [FUNCTIONS] Composite Functions

Condition & Range

9. [FUNCTIONS] Inverse Functions

Sketch of f and f inverse

10. [FUNCTIONS] Composite Functions

Range

11. [FUNCTIONS] Composite Functions + Inverse Functions

Question on Functions (Composite)

12. [FUNCTIONS] Composite Functions + Inverse Functions

Summary on taking/replacing inverse functions and sketching identity functions

13. [FUNCTIONS] Composite Functions + Inverse Functions

Question on Functions with identity function and algebraic method

14. [FUNCTIONS] Composite Functions + Inverse Functions

Inverse & Composite Functions

15. [FUNCTIONS] Composite Functions + Inverse Functions

Sketch of Inverse Composite Functions

16. [FUNCTIONS] Composite Functions + Inverse Functions

Composite Functions Identity Functions