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

Example 1Add / Subtract Functions a)b)

Example 2Multiply / Divide Functions a)b)

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

Example 4Composites of a Function Set a)

Example 4Composites of a Function Set b)

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

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

Example 1Inverses of Ordered Pair Relations a) b)

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

Example 2Find an Inverse Function a)b)

Example 2Continued 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.

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

Example 4One-to-One (Horizontal Line Test) Determine whether the functions are one-to-one. a)b) One-to-OneNot One-to-One