Review the following concepts if needed:
Combinations of Functions and Inverse Functions Practice Test
Problems
Problems 15 refer to and g ( x ) = 2 x + 4.

Find the domain for f + g ( x ).
(a) (3, ∞)
(b) (−∞, 3) ∪ (3, ∞)
(c) (−∞, 3] ∪ [3, ∞)
(d) [3, ∞)

Find f o g ( x ).

Find g o f ( x ).

Find f o g (4)
(a) 12
(c) 6
(d) 48

Find f ^{−1} ( x ).
(a) x − 3

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

Are and g ( x ) = 2 x − 3 inverses?
(a) Yes
(b) No
(c) Cannot be determined

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, ∞)

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
 B
 A
 C
 B
 C
 A
 B
 B
 B
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