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Unformatted text preview: 38 Chapter 1 Review
39. First piece: Line through (0, 1) and (1, 0) m y
0 1 1 0 1 1 34. (a) The function is defined for all values of x, so the domain is ( , ). x 2, which attains (b) The function is equivalent to y all nonnegative values. The range is [0, ). (c)
5 1 x x 1 or 1 Second piece: Line through (1, 1) and (2, 0) m
[ 8, 8] by [ 3, 3]
0 2 1 1 1 1 1 1 x 0 1 x x 1 2 y 3 0, so the domain is y f(x) (x x 1 2 1) 2 or 2 x, x, 35. (a) The logarithm requires x (3, ). (b) The logarithm attains all real values, so the range is ( , ). (c) 40. First piece: Line through (0, 0) and (2, 5) m y
[ 3, 10] by [ 4, 4]
5 2 5 x 2 0 0 5 2 Second piece: Line through (2, 5) and (4, 0) m y y f(x)
0 4 5 2 5 (x 2 5 x 2 5x , 2 5 2 5 2 36. (a) The function is defined for all values of x, so the domain is ( , ). (b) The cube root attains all real values, so the range is ( , ). (c) 2) 5
5x 2 10 or 10 0
5x , 2 x x 2 4 10 (Note: x
[ 10, 10] by [ 4, 4] 2 2 can be included on either piece.) f (g( 1)) g( f (2)) f ( f(x)) f g
1 2 1 x 1 1/x 37. (a) The function is defined for is [ 4, 4]. 4 x 4, so the domain 41. (a) ( f g)( 1) (b) (g f )(2) (c) ( f f )(x) f 1 1 1 1/2 + 2 2 f (1)
1 2.5 1 1 1
2 5 x , 4 x 4, (b) The function is equivalent to y which attains values from 0 to 2 for x in the domain. The range is [0, 2]. (c) or x, x 0
1 (d) (g g)(x) g(g(x))
4 g
2 x 2 1 x 2 1/ x 2 2 x 2 [ 6, 6] by [ 3, 3] 1 38. (a) The function is defined for is [ 2, 2]. (c) 2 x 2, so the domain 42. (a) ( f g)( 1) f (g( 1)) f(
3 (b) See the graph in part (c). The range is [ 1, 1]. 1 2 g(2 f (2 g(
3 1) 0 2) x) x 1) 2 g(0) 2 (2
3 3 3 f (0) (b) (g f )(2) (c) ( f f )(x)
[ 3, 3] by [ 2, 2] g( f (2)) f ( f (x)) g(g(x)) 0 1 x 1 1 1 x) x (d) (g g)(x) ...
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 Spring '08
 GERMAN

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