Domains%20and%20Inverse%20Functions

1
DomainsandInverse Functions

• Sections 1.7 and 1.8

2
Objectives

• Determine the domain and range (where possible)
  of a function given as an equation.
• Determine if a function given as an equation is
  one-to-one.
• Determine if a function given as a graph is
  one-to-one.
• Algebraically find the inverse of a one-to-one
  function given as an equation.

3
Objectives

• State the domain and range of a function and it
  inverse.
• State the relationships between the domain and
  range of a function and its inverse
• Restrict the domain of a function that is not
  one-to-one so that an inverse function can be
  found.
• Draw the graph of the inverse function given the
  graph of the function.

4
Vocabulary

• inverse function
• horizontal line test
• function composition
• one-to-one function

5
Domain Questions

• Does the function have a denominator?
• Does the function have a square or even root?
• Does the function have a log or ln in it?
• Did the function arise from finding an inverse?
• Is this a real world problem?

6
Find the domain of the function
7
Find the domain of the function
8
Find the domain of the function
9
Find the domain of the function
10
Given the functions and
find each of the following
11
Determine if the function is one-to-one.
12
Steps for finding an inverse function.

1. Change the function notation f(x) to y.
2. Change all the xs to ys and ys to xs.
3. Solve for y.
4. Replace y with f -1(x).

13
Find the inverse of the function
Find the domains of the function and its inverse.
14
Find the inverse of the function
Find the domains of the function and its inverse.
15
Find the inverse of the function
Find the domains of the function and its inverse.
16
Find the inverse of the function
Find the domains of the function and its inverse.
17
Draw the graph of the inverse function for the
graph of f(x) shown below.
18
The function is not one-to-one.  Choose
the largest possible domain containing the number
100 so that the function restricted to the domain
is one-to-one.  Find the inverse function for
that restricted function.