1. Composite & Inverse Functions
Honors Precalculus
October 17, 2017
Mr. Agnew

2. Essential Question Essential Vocabulary
How do you find the inverse of a function?
How do you evaluate a function composition?
Essential Vocabulary
One-to-one function
Inverse Function
Function Composition

3. Composition of Functions
One function is the input of another function.
Plug “inside” function into x in “outside” function.
f(g(x)) (f g)(x)

4. Domain of Functions
The domain of a function includes all of the x values that can be plugged into x.
In a composite function, the domain includes restrictions of all functions involved in the composition. (The original functions and the composite.)
Guided Practice, if needed

5. One-to-One Functions What is a one-to-one function?
A relation in which every x value is matched to exactly one y value (function) and every y value is matched to exactly one x value (one-to-one).
How do we determine if a function is one-to-one?

6. Inverse Relations To have an inverse, a function must be one-to-one.
The inverse of a function switches all the x and y values.
The graph of an inverse is a reflection over the line y = x.

7. Finding Inverses To find the inverse of a given function:
Switch the x and y
Solve for y
Label inverse with f -1(x)
Page #44 – 48, 52, 56, 60, 66, 70, 74

8. To Make You Think…
1. Is the inverse of a function a function? 2. Do all functions have inverses? 3. Do all linear functions have inverses? 4. What is the slope of the inverse of a linear function?

9. Homework: 10/17/17
Pages # 8, 10, 17, 32, 38, 40 Page 269 – 270 #43, 45, 51, 55, 63, 67, 73, 75, 77, 81