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Operations on Functions

Operations on Functions. Composite Function:. Combining a function within another function. Written as follows:. Operations Notation :. Sum:. Difference:. Product:. Quotient:. Example 1 Add / Subtract Functions. a). b). Example 2 Multiply / Divide Functions. a). b).

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Operations on Functions

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  1. Operations on Functions Composite Function: Combining a function within another function. Written as follows: Operations Notation: Sum: Difference: Product: Quotient:

  2. Example 1 Add / Subtract Functions a) b)

  3. Example 2 Multiply / Divide Functions a) b)

  4. Example 3 Evaluate Composites of Functions Recall: (a + b)2 = a2 + 2ab + b2 a) b)

  5. Example 4 Composites of a Function Set a)

  6. Example 4 Composites of a Function Set b)

  7. Inverse Properties: 1] 2] Inverse Functions and Relations Inverse Relation: Relation (function) where you switch the Domain and range values Inverse Notation:

  8. [3] Solve for y and replace it with Steps to Find Inverses [1] Replace f(x) with y [2] Interchange x and y One-to-One: A function whose inverse is also a function (horizontal line test) Inverse is not a function

  9. b) Example 1 Inverses of Ordered Pair Relations a)

  10. Inverses of Graphed Relations The graphs of inverses are reflections about the line y=x

  11. Example 2 Find an Inverse Function a) b)

  12. Example 2 Continued c) d) Inverse is not a 1-1 function. (BUT the inverse is 2 different functions: If you restrict the domain in the original function, then the inverse will become a function.

  13. Example 3 Verify two Functions are Inverses a) Method 1 b) Method 2 Yes, Inverses Yes, Inverses

  14. Example 4 One-to-One (Horizontal Line Test) Determine whether the functions are one-to-one. a) b) One-to-One Not One-to-One

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