Solved Composition of Functions Worksheet Let f(x) = 2x - 1 ... - Free Printable

Let’s solve each problem step by step. We’ll use the given functions:

Section I:
- f(x) = 2x - 1
- g(x) = 3x
- h(x) = x² + 1

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1. f(g(-3))

First, find g(-3):
g(-3) = 3 × (-3) = -9

Now plug into f:
f(-9) = 2×(-9) - 1 = -18 - 1 = -19

✔ Answer: -19

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2. f(h(7))

First, find h(7):
h(7) = 7² + 1 = 49 + 1 = 50

Now plug into f:
f(50) = 2×50 - 1 = 100 - 1 = 99

✔ Answer: 99

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3. g(h(24))

First, find h(24):
h(24) = 24² + 1 = 576 + 1 = 577

Now plug into g:
g(577) = 3 × 577 = let’s compute:
3 × 500 = 1500
3 × 77 = 231
Total = 1500 + 231 = 1731

✔ Answer: 1731

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4. h(f(9))

First, find f(9):
f(9) = 2×9 - 1 = 18 - 1 = 17

Now plug into h:
h(17) = 17² + 1 = 289 + 1 = 290

✔ Answer: 290

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5. g(f(0))

First, find f(0):
f(0) = 2×0 - 1 = 0 - 1 = -1

Now plug into g:
g(-1) = 3 × (-1) = -3

✔ Answer: -3

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6. h(g(-4))

First, find g(-4):
g(-4) = 3 × (-4) = -12

Now plug into h:
h(-12) = (-12)² + 1 = 144 + 1 = 145

✔ Answer: 145

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7. f(g(h(2)))

Start from inside: h(2)
h(2) = 2² + 1 = 4 + 1 = 5

Then g(5) = 3 × 5 = 15

Then f(15) = 2×15 - 1 = 30 - 1 = 29

✔ Answer: 29

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8. h(g(f(5)))

Start with f(5):
f(5) = 2×5 - 1 = 10 - 1 = 9

Then g(9) = 3×9 = 27

Then h(27) = 27² + 1 = 729 + 1 = 730

✔ Answer: 730

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9. g(f(h(-6)))

Start with h(-6):
h(-6) = (-6)² + 1 = 36 + 1 = 37

Then f(37) = 2×37 - 1 = 74 - 1 = 73

Then g(73) = 3×73 = 219

✔ Answer: 219

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Section II:
New functions:
- f(x) = 9 - x
- g(x) = x² + x
- h(x) = x - 2

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10. g(f(3))

First, f(3) = 9 - 3 = 6

Then g(6) = 6² + 6 = 36 + 6 = 42

✔ Answer: 42

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11. f(g(4))

First, g(4) = 4² + 4 = 16 + 4 = 20

Then f(20) = 9 - 20 = -11

✔ Answer: -11

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12. h(f(-6))

First, f(-6) = 9 - (-6) = 9 + 6 = 15

Then h(15) = 15 - 2 = 13

✔ Answer: 13

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13. f(h(-3))

First, h(-3) = -3 - 2 = -5

Then f(-5) = 9 - (-5) = 9 + 5 = 14

✔ Answer: 14

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14. h(g(11))

First, g(11) = 11² + 11 = 121 + 11 = 132

Then h(132) = 132 - 2 = 130

✔ Answer: 130

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15. g(h(-9))

First, h(-9) = -9 - 2 = -11

Then g(-11) = (-11)² + (-11) = 121 - 11 = 110

✔ Answer: 110

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16. g(h(f(5)))

Start with f(5) = 9 - 5 = 4

Then h(4) = 4 - 2 = 2

Then g(2) = 2² + 2 = 4 + 2 = 6

✔ Answer: 6

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17. h(g(f(13)))

Start with f(13) = 9 - 13 = -4

Then g(-4) = (-4)² + (-4) = 16 - 4 = 12

Then h(12) = 12 - 2 = 10

✔ Answer: 10

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18. f(g(h(-8)))

Start with h(-8) = -8 - 2 = -10

Then g(-10) = (-10)² + (-10) = 100 - 10 = 90

Then f(90) = 9 - 90 = -81

✔ Answer: -81

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Final Answer:
1. -19
2. 99
3. 1731
4. 290
5. -3
6. 145
7. 29
8. 730
9. 219
10. 42
11. -11
12. 13
13. 14
14. 130
15. 110
16. 6
17. 10
18. -81