Quiz f(x) = 2x + 3 and f(g(x)) = ? (f + g)(x) = ? 3. What is the domain? 3 f(x) - 2 g(x) = ? 4.

Tonight’s Homework: 6-4: (page 442) (evens): 4 – 12, 16 – 20, 46, 50, 52, 58, 64 (13 points) (13 points) Now, come on; you CAN DO 13 problems!!

Section 6-4 Inverse Functions

Vocabulary Inverse Relation: A relation that interchanges the input and output values of the original relation. the input and output values of the original relation. (-2, 5), (5, 6), (-2, 6), (7, 6) Relation: Inverse Relation: (5, -2), (6, 5), (6, -2), (6, 7)

Graphs of Inverse Relations y = x Each point in the inverse relation is a point from the relation is a point from the relation reflected across the line y = x reflected across the line y = x

How to find the inverse relation Relation: y = 0.5x Exchange ‘x’ and ‘y’ in the original relation. x = 0.5y Solve for ‘y’ (get ‘y’ all by itself). y = 2x - 4

How to find the inverse relation Relation: 1. Exchange ‘x’ and ‘y’ in the original relation. 2. Solve for ‘y’ (get ‘y’ all by itself).

Your Turn: Find the inverse of: 1. y = x – 2 2. y = 4x

How to write: “the inverse of f(x)” This means, “what is the inverse function of f(x)?.

Composition of Functions (review) 4. f(g(x)) = ? 5. g(f(x)) = ?

How can you tell if functions are inverses of each other? f(x) = 0.5x + 2 g(x) = 2x - 4 IF: f(g(x)) = x and g(f(x)) = x then f(x) and g(x) are inverses of each other. then f(x) and g(x) are inverses of each other. f(g(x)) = f(2x – 4) = 0.5(2x – 4) + 2 = x g(f(x)) = g(0.5x + 2) = 2(0.5x + 2) - 4 = x

Your Turn: 6. Are f(x) and g(x) inverses of each other ? 7. Are f(x) and g(x) inverses of each other ?

Inverses of Non –Linear Functions

If you have the graph of a relation; what is the test to determine if the relation is a function? Vertical Line Test if the line intersects the graph more than once, it is NOT a function. if the line intersects the graph more than once, it is NOT a function.

How can you tell if the inverse of a function is a function? Horizontal Line Test: if the line intersects the graph more than once, then the Inverse of the function is NOT a function.

Solving for ‘x’ What do I do to get ‘x’ = ‘x’ = (some number) Take ‘square root’ of each side. of each side. What is the “equivalent” exponent that I should “take each side to” that is the same as taking “take each side to” that is the same as taking the square root of each side? the square root of each side?

Another example 1. Exchange ‘x’ and ‘y’ in the original relation. 2. Solve for ‘y’ (get ‘y’ all by itself). Oops, I don’t see any ‘y’ to exchange with ‘x’!!! Remember: f(x) = y

Your Turn: 8. 9.

Using the idea of an inverse function to “undo” a function Isolate the power: undo the power

Your Turn: 10. Solve 11. Solve

Using an inverse function to solve an equation. Ticket prices in the NFL can be modeled by: where ‘t’ is the number of years since years since During what year was the price of a ticket $50.85 ? (price as a function of time since 1995)

Tonight’s Homework: 6-4: (evens): 4 – 12, 16 – 28, 34, 36, 52, 56, 58, 62 (18 points) 56, 58, 62 (18 points)