a. Write a function, f(x), to represent the 5 bonus points. Warm Up: A math test has a bonus question.  The directions simply state that if you answer the question correctly you will receive 5 bonus points and then your test grade will be increased by 7%. (Let x = test score before answering the bonus question.) a.  Write a function, f(x), to represent the 5 bonus  points. b.  Write a function, g(x), to represent just the percent of increase. c.  Explain the meaning of g(f(x)). d.  Find g(f(75))

Lesson 1.5-1 Inverse Functions Objective: Define inverse functions and algebraically verify that two functions are inverses.

NOTE: The inverse of a function may not always be a function! Notation: NOTE: The inverse of a function may not always be a function!

Ex. 1: Calculate the inverse of the following functions

Ex. 2: Calculate the inverse of the following functions 1 -2 -1 3 4 f(x) 2 x f-1(x)

Two Functions are inverses if: The domain of f is equal to the range of f -1, and the range of f is equal to the domain of f -1.

To verify that two functions are inverses:

Ex. 3: Determine if the functions are inverses

Ex. 4: Determine if the functions are inverses

Ex. 5: Determine if the functions are inverses

Graphs of Inverse Functions

Graph the inverse points…

Ex. 6: Determine if the inverse is a function

Horizontal Line Test: Determines if the function is invertible

Ex. 7: Use a graphing calculator to see if an inverse function exists

Ex. 8: Find the inverse algebraically

Ex. 9: Find the inverse algebraically

Ex. 10: Find the inverse algebraically

Ex. 11: Find and verify the inverse of the given function

Closing Thoughts: Synthesis Calculate, verify, and graph the inverse.