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Find (f g)(x) for each set of functions:
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2. Splash Screen

3. Lesson 7-1 Polynomial Functions
Lesson 7-2 Graphing Polynomial Functions
Lesson 7-3 Solving Equations Using Quadratic Techniques
Lesson 7-4 The Remainder and Factor Theorems
Lesson 7-5 Roots and Zeros
Lesson 7-6 Rational Zero Theorem
Lesson 7-7 Operations on Functions
Lesson 7-8 Inverse Functions and Relations
Lesson 7-9 Square Root Functions and Inequalities
Contents

4. Example 1 Find an Inverse Relation Example 2 Find an Inverse Function
Example 3 Verify Two Functions are Inverses
Lesson 8 Contents

5. Geometry The ordered pairs of the relation {(1, 3), (6, 3), (6, 0), (1, 0)} are the coordinates of the vertices of a rectangle. Find the inverse of this relation and determine whether the resulting ordered pairs are also the coordinates of the vertices of a rectangle.
To find the inverse of this relation, reverse the coordinates of the ordered pairs. The inverse of the relation is {(3, 1), (3, 6), (0, 6), (0, 1)}.
Example 8-1a

6. Answer: Plotting the points shows that the ordered pairs also describe the vertices of a rectangle. Notice that the graph of the relation and the inverse are reflections over the graph of y = x.
Example 8-1b

7. Geometry The ordered pairs of the relation {(–3, 4), (–1, 5), (2, 3), (1, 1), (–2, 1)} are the coordinates of the vertices of a pentagon. Find the inverse of this relation and determine whether the resulting ordered pairs are also the coordinates of the vertices of a pentagon.
Answer: {(4, –3), (5, –1), (3, 2), (1, 1), (1, –2)} These ordered pairs also describe the vertices of a pentagon.
Example 8-1c

8. Step 1 Replace f (x) with y in the original equation.
Find the inverse of
Step 1 Replace f (x) with y in the original equation.
Step 2 Interchange x and y.
Example 8-2a

9. Step 4 Replace y with f –1(x).
Step 3 Solve for y.
Inverse
Multiply each side by –2.
Add 2 to each side.
Step 4 Replace y with f –1(x).
Example 8-2b

10. Answer: The inverse of is
Example 8-2c

11. Graph the function and its inverse.
Graph both functions on the coordinate plane. The graph of is the reflection for over the line
Example 8-2d

12. Answer:
Example 8-2e

13. b. Graph the function and its inverse. Answer:
a. Find the inverse of
b. Graph the function and its inverse.
Answer:
Answer:
Example 8-2f

14. Determine whether and are inverse functions.
Check to see if the compositions of f (x) and g (x) are identity functions.
Example 8-3a

15. Answer: The functions are inverses since both and equal x.
Example 8-3b

16. Determine whether and are inverse functions.
Answer: The functions are inverses since both compositions equal x.
Example 8-3c