Combinations of Functions and Inverse Functions Practice Test

Review the following concepts if needed:

• Combinations of Functions Help
• Inverse Functions Help

Combinations of Functions and Inverse Functions Practice Test

Problems

Problems 1-5 refer to and g ( x ) = 2 x + 4.

1. Find the domain for f + g ( x ).

   (a) (3, ∞)

   (b) (−∞, 3) ∪ (3, ∞)

   (c) (−∞, 3] ∪ [3, ∞)

   (d) [3, ∞)

2. Find f o g ( x ).

   

3. Find g o f ( x ).

   

4. Find f o g (4)

   (a) 12

   

   (c) 6

   (d) 48

5. Find f ⁻¹ ( x ).

   (a) x − 3

6. The graph of f ( x ) is given in Figure 4.13. Does f ( x ) have an inverse?

   (a) Yes

   (b) No

   (c) Cannot be determined 

   

   Fig. 4.13 .

7. Are and g ( x ) = 2 x − 3 inverses?

   (a) Yes

   (b) No

   (c) Cannot be determined

8. What is the domain for f o g ( x ) where

   

   (a) (−∞, −2) ∪ (−2, 0) ∪ (0, 2) ∪ (2, ∞)

   (b) (−∞, −2) ∪ (−2, 2) ∪ (2, ∞)

   (c) (−∞, 0) ∪ (0, 2) ∪ (2, ∞)

   (d) (−∞, −2) ∪ (−2, 0) ∪ (0, ∞)

   

   Fig. 4.14

9. The solid graph in Figure 4.14 is the graph of f ( x ). The dashed graph is the graph of g ( x ). Find f o g (4).

   (a) −2

   (b) −3

   (c) 2

   (d) 3

Solutions

1. B
2. A
3. C
4. B
5. C
6. A
7. B
8. B
9. B