2 – 2 Function Operations
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Let 𝑓(𝑥) = 7𝑥 + 5 and 𝑔(𝑥) = 𝑥 2 . Perform each function operation and find their domain.
1. (𝑓 + 𝑔)(𝑥)
2. (𝑓 − 𝑔)(𝑥)
3. (𝑔 − 𝑓)(𝑥)
4. (𝑓 ∙ 𝑔)(𝑥)
Let 𝑓(𝑥) = 2𝑥 2 + 𝑥 − 3 and 𝑔(𝑥) = 𝑥 − 1. Perform each function operation and find their domain.
5. (𝑓 + 𝑔)(𝑥)
6. (𝑓 − 𝑔)(𝑥)
7. (𝑔 − 𝑓)(𝑥)
8. (𝑓 ∙ 𝑔)(𝑥)
Let 𝑓(𝑥) = 2𝑥 + 5 and 𝑔(𝑥) = 𝑥 2 − 3𝑥 + 2. Perform each function operation and find their
domain.
9. 𝑓(𝑥) + 𝑔(𝑥)
10. 3𝑓(𝑥) − 2
11. 𝑔(𝑥) − 𝑓(𝑥)
12. −2𝑔(𝑥) + 𝑓(𝑥)
13. 𝑓(𝑥) − 𝑔(𝑥) + 10
14. 4𝑓(𝑥) + 2𝑔(𝑥)
2 – 3 Composition of Functions
Let 𝑔(𝑥) = 2𝑥 and ℎ(𝑥) = 𝑥 2 + 4. Find each value or expression.
15. (ℎ ∘ 𝑔)(1)
16. (ℎ ∘ 𝑔)(−5)
17. (𝑔 ∘ ℎ)(−2)
18. (𝑔 ∘ ℎ)(0)
20. (𝑔 ∘ 𝑔)(𝑎)
19. (𝑔 ∘ ℎ)(𝑎)
21. (ℎ ∘ 𝑔)(𝑎)
Let 𝑓(𝑥) = 𝑥 2 and 𝑔(𝑥) = 𝑥 − 3. Find each value or expression.
22. (𝑔 ∘ 𝑓)(−2)
23. (𝑓 ∘ 𝑔)(−2)
24. (𝑔 ∘ 𝑓)(3.5)
25. (𝑓 ∘ 𝑔)(3.5)
Let 𝑔(𝑥) = 3𝑥 + 2 and 𝑓(𝑥) =
𝑥−2
3
. Find each value.
26. 𝑓(𝑔(1))
27. 𝑔(𝑓(−4))
28. 𝑓(𝑔(0))
29. 𝑔(𝑓(2))
30. 𝑔(𝑔(0))
31. (𝑔 ∘ 𝑔)(1)
32. (𝑓 ∘ 𝑔)(−2)
33. (𝑓 ∘ 𝑓)(0)
For each pair of functions, find 𝑓(𝑔(𝑥)) 𝑎𝑛𝑑 𝑔(𝑓(𝑥))
34. 𝑓(𝑥) = 3𝑥 2 + 2, 𝑔(𝑥) = 2𝑥
35. 𝑓(𝑥) =
𝑥−3
2
, 𝑔(𝑥) = 2𝑥 − 3
Inverse Relations and Functions
Find the inverse of each relation.
36.
37.
𝑥
𝑦
1
0
2
1
3
0
4
2
𝑥
𝑦
0
0
1
1
2
4
3
9
Find the inverse of each function. Is the inverse a function?
38. 𝑦 = 3𝑥 + 1
39. 𝑦 = 2𝑥 − 1
Graph each relation and its inverse.
41. 𝑦 = 2𝑥 − 3
40. 𝑦 = 4 − 3𝑥
42. 𝑦 = 3 − 7𝑥
y
y
x
x
y
43. 𝑦 = −𝑥
x