Sec' 2'8 Inverse Functions

1

• Sec. 2.8 Inverse Functions
• One-to-One Functions
• A function f with domain A is called a
  one-to-one function if no two values of x
  have the same image (value of f(x)).
• whenever
• If , then
• No Horizontal line intersects the graph more than
  one time.

2

• Deciding if a function is One-to-One
• Which of the following are one-to-one

3

• Deciding if a function is One-to-One
• Is the following function one-to-one?

4

• Inverse of a one-to-one function
• Let be a one-to-one function with Domain
  A and Range B. Then we can define its inverse
  function with Domain B and Range A by
• An inverse function undoes the rule that a
  function does.
• If a function multiplies by 2, the inverse
  divides by 2.
• If a function takes radius and gives area,
  the inverse takes area and gives the
  corresponding radius.
• If a function takes degrees Fahrenheit and gives
  degrees Celsius, then the inverse takes Celsius
  and gives Fahrenheit.

5

• Showing two functions are inverses of each other

• Finding the inverse of a one-to-one function
• Write
• Solve the equation for y in terms of x (if
  possible)
• Interchange x and y to get

6

• Finding the inverse of a one-to-one function

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• Comparing the graph of a function and its inverse
• The graph of is obtained by
  reflecting the graph of in the line
  .

8

• HW Section 2.8
• 27 Show that the two functions are inverses of
  each other.

9

• HW Section 2.8
• 41 Find the inverse function of f.

10

• HW Section 2.8
• 53 Sketch the graph. Then sketch its inverse.
  Then find the equation for the inverse function.