Inverse Functions
Objective: In this lesson you learned how to find
inverse functions
graphically and algebraically .
Important Vocabulary Define each term or
concept. Inverse function Horizontal Line Test |
I. Inverse Functions (Pages 237-238)
For a function f that is defined by a set of ordered pairs , to form
the inverse function of f, . . .
What you should learn
How to find inverse
functions informally and
verify that two functions
are inverse functions of
each other
For a function f and its inverse f^{-1}, the domain of f is
equal to
___________________, and the range of f is equal to
___________________.
To verify that two functions , f and g, are inverse
functions of
each other, . . .
Example 1: Verify that the functions f (x) = 2x - 3
and
are inverse functions of each other.
II. The Graph of an Inverse Function (Page 239)
If the point (a, b) lies on the graph of f , then the point
(_____________) must lie on the graph of f ^{-1} and vice versa. The
graph of f ^{-1} is a reflection of the graph of f in the line
What you should learn
How to use graphs of
functions to determine
whether functions have
inverse functions
III. One -to-One Functions (Page 240)
To tell whether a function has an inverse function from
its
graph , . . .
What you should learn
How to use the
Horizontal Line Test to
determine if functions are
one-to-one
A function f is one-to-one if . . .
A function f has an inverse function if and only if f is _____________
Example 2: Does the graph of the function at the
right have
an inverse function? Explain.
IV. Finding Inverse Functions Algebraically (Pages 241-242)
To find the inverse of a function f algebraically , . . .
1)
2)
3)
4)
5)
What you should learn
How to find inverse
functions algebraically
Example 3: Find the inverse (if it exists) of f (x) = 4x - 5 .
Homework Assignment
Page(s)
Exercises
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