Operations and Compositions of Functions :-)

[Pages:10]Math 5 SN

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Operations and Compositions of Functions :-)

Perform the indicated operation.

1) g(a) = 4a - 1 h(a) = a2 + 5 Find g(h(a))

2) f (x) = 2x - 1 g(x) = -3x2 - 2x Find ( f g)(x)

3) g(n) = -n - 3 h(n) = n2 + 1

Find (g h)(n)

4) h(n) = -n - 1 g(n) = n2 - n

Find (h g)(n)

5) h(t) = -2t - 5 g(t) = -3t2 - 2t Find h(g(t))

6) f (a) = a - 2 g(a) = -3a2 - 1 Find ( f g)(a)

7) g(x) = 2x - 5 f (x) = 4x + 2 Find g( f (x))

8) h(x) = -3x - 3 g(x) = x3 + 2x2

Find (h g)(x)

9) g(a) = a2 + 3 h(a) = 4a + 4 Find g(h(a))

10) f (x) = x2 + 5 g(x) = 3x + 3 Find f (g(x))

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11) g(x) = x3 - 1 h(x) = -2x - 5 Find g(h(x))

13) g(n) = 4n - 4 f (n) = 4n + 4 Find (g f )(n)

15) f (x) = 2x - 4 g(x) = x + 3 Find f (g(x))

17) f (x) = 3x - 5 Find f ( f (x))

19) g(n) = 3n - 4 f (n) = n3 - 2n Find (g f )(n)

21) f (x) = 3x g(x) = x - 5 Find f (x) + g(x)

12) h(x) = -3x2 - 2x g(x) = 2x + 3 Find (h g)(x)

14) g(x) = 3x - 1 h(x) = -3x3 - 3x2 Find g(h(x))

16) g(x) = 4x + 5 f (x) = 2x - 2 Find (g f )(x)

18) h(x) = -3x2 - 4x g(x) = x + 5 Find h(g(x))

20) g(x) = 4x h(x) = x3 + 5x2 Find g(h(x))

22) f (n) = -3n + 2 g(n) = 4n + 2 Find f (n) g(n)

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23) f (n) = 3n + 1 g(n) = n2 + 4n Find ( f - g)(n)

25) g(a) = 3a + 1 h(a) = 4a + 2 Find g(a) ? h(a)

27) f (n) = -2n - 2 g(n) = 3n - 4 Find f (n) g(n)

29) g(x) = 2x + 1 h(x) = x3 + 2x Find (g + h)(x)

31) f (a) = a2 - 3 g(a) = a - 4 Find f (a) g(a)

33) g(n) = 4n - 4 f (n) = n2 + 4n Find g(n) + f (n)

24) g(a) = 2a - 5 h(a) = a3 - a Find g(a) + h(a)

26) f (n) = 2n g(n) = n2 - 5 Find f (n) - g(n)

28) g(x) = x2 + 3 h(x) = -4x

( ) Find g (x) h

30) g(x) = 3x3 + 3x h(x) = 2x - 2 Find g(x) ? h(x)

32) g(t) = 3t + 3 f (t) = t + 5 Find g(t) f (t)

34) h(n) = 4n - 4 g(n) = n3 + 1 Find h(n) + g(n)

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35) g(t) = t + 2 f (t) = t + 1 Find g(t) + f (t)

37) f (a) = a - 4 g(a) = a2 - a

( ) Find f (a) g

39) h(a) = -a3 - 2a g(a) = 4a + 3 Find h(a) - g(a)

41) f (n) = 3n - 4 g(n) = 2n - 1 Find (4 f - g)(n)

43) f (x) = x + 5 g(x) = x3 - x2 + x Find ( f - 3g)(x)

45) f (x) = -x2 + 5 g(x) = 2x Find 2 f (x) + 3g(x)

36) h(n) = 3n + 5 g(n) = n + 3 Find (h - g)(n)

38) h(x) = x2 - 5 g(x) = 3x + 3 Find h(x) + g(x)

40) f (x) = 2x - 4 g(x) = -x2 - x Find f (x) ? g(x)

42) g(x) = x + 4 f (x) = 3x2 + 5 Find -5g(x) - 3 f (x)

44) g(n) = 3n - 5 h(n) = n2 - 5n Find (4g + 4h)(n)

46) h(x) = 2x3 + x2 g(x) = 3x + 5 Find 2h(x) + 2g(x)

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47) f (x) = x2 - x g(x) = 3x + 2 Find (2 f - 4g)(x)

49) h(n) = n + 1 g(n) = n2 - 1 Find h(n) - 2g(n)

51) f (n) = n - 4 g(n) = 2n Find 3 f (n) + 5g(n)

53) f (n) = -4n - 3 g(n) = n2 - 3n Find 5 f (n) - g(n)

55) h(t) = 2t2 + 2t g(t) = -t - 4 Find (3h + 2g)(t)

57) g(t) = 2t - 5 f (t) = t3 + 3t Find (3g + f )(t)

48) g(a) = 4a - 4 f (a) = 4a + 1 Find -3g(a) - 5 f (a)

50) g(x) = 3x - 3 h(x) = x3 - 4x Find (5g - 3h)(x)

52) h(x) = -2x + 4 g(x) = x3 - 2x Find (4h + g)(x)

54) g(x) = 2x + 2 f (x) = x3 + 5 Find (3g - 3 f )(x)

56) f (x) = -3x2 + 4 + 2x g(x) = 4x - 5 Find 3 f (x) - g(x)

58) g(t) = -t2 + 4 h(t) = -t - 2 Find (3g - 4h)(t)

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59) g(x) = 2x + 3 f (x) = x - 4 Find g(x) - 4 f (x)

61) f (n) = -n - 5 g(n) = n - 3 Find f (g(-3))

63) g(x) = x2 + 5x h(x) = 3x - 3 Find (g - h)(-10)

65) g(n) = 2n - 4 h(n) = -2n + 2 Find (g - 5h)(4)

67) f (x) = 4x + 2 g(x) = 2x + 4 Find f (-9) + g(-9)

69) g(n) = 3n + 3 h(n) = 2n + 3 Find g(-9) ? h(-9)

60) h(x) = x3 - 5x2 g(x) = 4x - 5 Find (2h - 2g)(x)

62) f (x) = x2 - 1 g(x) = -4x Find f (7) - 2g(7)

64) g(t) = 4t - 4 h(t) = -t3 - 5t2 Find g(-5) h(-5)

66) f (x) = x + 4 g(x) = 2x + 2 Find ( f + g)(-8)

68) g(t) = t2 + 2t h(t) = 3t - 3 Find g(0) h(0)

70) f (x) = 3x + 1 g(x) = x3 - x Find ( f - g)(-1)

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71) f (t) = -2t g(t) = t2 - 4t Find ( f - g)(9)

73) h(n) = -2n + 3 g(n) = 4n Find (h g)(-2)

75) g(x) = x2 - 2 - x h(x) = 2x - 2 Find (5g + 2h)(-2)

77) f (t) = 2t - 1 g(t) = 3t - 3 Find f (6) g(6)

79) h(x) = 4x - 1 g(x) = x2 - x Find (h + g)(7)

81) f (t) = -3t - 4 g(t) = 2t Find f (-2t) - g(-2t)

72) g(n) = -3n2 + 2n f (n) = n + 2 Find g(10) ? f (10)

74) f (a) = 3a - 3 g(a) = -2a2 + 6a Find (-5 f - 2g)(6)

76) h(x) = 3x - 1 g(x) = x2 - 1 Find h(9) + g(9)

78) g(n) = n2 + 5n h(n) = -4n Find (g h)(-4)

80) g(a) = 4a - 2 h(a) = a3 + 3a2

( ) Find g (-5) h

82) g(x) = 2x - 4 f (x) = 4x + 3 Find g( f (3 + x))

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83) f (n) = 4n - 5 g(n) = n + 4 Find ( f - g)(n + 3)

85) f (n) = 2n + 1 g(n) = n2 + n

( ) ( ) Find f n g n 33

87) f (a) = 3a2 - 1 g(a) = 2a - 5 Find f (z2) g(z2)

89) g(n) = 3n + 3 f (n) = -n - 2 Find g(-4n) + f (-4n)

91) h(a) = 2a - 4 g(a) = a3 - 5a2 Find 2h(-a) + 2g(-a)

84) g(x) = x3 - 5x2 - x f (x) = x + 1 Find g( f (x2 ))

86) g(a) = 4a - 3 h(a) = a2 + 2a Find g(z - 4) ? h(z - 4)

88) g(t) = -t + 4 f (t) = 4t - 3 Find g(4t) + f (4t)

90) f (x) = x + 5 g(x) = 2x - 5

( ) Find f (2b) g

92) f (a) = 2a + 4 g(a) = 3a + 4 Find f (-4a) ? g(-4a)

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