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# Combinations of Functions and Inverse Functions Practice Test

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## 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

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