Dr. Nermien Ismail American School
Grade 11
Q3 W1
Operations with Functions
A. Given f(x)  4x2  1 and
Math. Department
CW1
g(x)  2x  1, find each function.
1. (f  g)(x)
2. (f  g)(x)
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3. (fg)(x)
4.
f
x
g
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5. f (g(x))
6. g (f (x))
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B. Use the following functions for Exercises 1–18.
f(x)  x
g(x)  x  3
h(x)  x2  9
k(x)  2x
Find each function.
1. (gk)(x)
 g(x) · k(x)
 (x  3)(2x)
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4.
k 
 f x
 
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2. (g  k)(x)
3. (k  f)(x)
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5. (hk)(x)
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6.
h
 x
g
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7. (h  f)(x)
8. (g  k)(x)
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9. (g  h)(x)
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Find each value.
10. g(h(10))
 g(102  9)
11. g(f (1))
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12. f (g(2))
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13. g(k(3))
14. h(g(3))
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15. h(k(3))
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16. k(f (2))
17. k(g(0))
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18. k(h(1))
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C. Given f (x)  4x  1 and g  x   x  3 .
a. Find f (g(x)).
f  g  x   f

b. Find g(f (x)).
x 3

g(f (x))  g(4x  1)
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D. Given h(x)  2x  1 and k(x)  3x2.
a. Find h(k(x)).
b. Find k(h(x)).
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Multiple Choice
Identify the choice that best completes the statement or answers the question.
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