Uploaded by Miss Washington

2.1-2.4

advertisement
2 – 2 Function Operations
Name_____________________________ date_________
Let 𝑓(π‘₯) = 7π‘₯ + 5 and 𝑔(π‘₯) = π‘₯ 2 . Perform each function operation and find their domain.
1. (𝑓 + 𝑔)(π‘₯)
2. (𝑓 − 𝑔)(π‘₯)
3. (𝑔 − 𝑓)(π‘₯)
4. (𝑓 βˆ™ 𝑔)(π‘₯)
Let 𝑓(π‘₯) = 2π‘₯ 2 + π‘₯ − 3 and 𝑔(π‘₯) = π‘₯ − 1. Perform each function operation and find their domain.
5. (𝑓 + 𝑔)(π‘₯)
6. (𝑓 − 𝑔)(π‘₯)
7. (𝑔 − 𝑓)(π‘₯)
8. (𝑓 βˆ™ 𝑔)(π‘₯)
Let 𝑓(π‘₯) = 2π‘₯ + 5 and 𝑔(π‘₯) = π‘₯ 2 − 3π‘₯ + 2. Perform each function operation and find their
domain.
9. 𝑓(π‘₯) + 𝑔(π‘₯)
10. 3𝑓(π‘₯) − 2
11. 𝑔(π‘₯) − 𝑓(π‘₯)
12. −2𝑔(π‘₯) + 𝑓(π‘₯)
13. 𝑓(π‘₯) − 𝑔(π‘₯) + 10
14. 4𝑓(π‘₯) + 2𝑔(π‘₯)
2 – 3 Composition of Functions
Let 𝑔(π‘₯) = 2π‘₯ and β„Ž(π‘₯) = π‘₯ 2 + 4. Find each value or expression.
15. (β„Ž ∘ 𝑔)(1)
16. (β„Ž ∘ 𝑔)(−5)
17. (𝑔 ∘ β„Ž)(−2)
18. (𝑔 ∘ β„Ž)(0)
20. (𝑔 ∘ 𝑔)(π‘Ž)
19. (𝑔 ∘ β„Ž)(π‘Ž)
21. (β„Ž ∘ 𝑔)(π‘Ž)
Let 𝑓(π‘₯) = π‘₯ 2 and 𝑔(π‘₯) = π‘₯ − 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(π‘₯) = 3π‘₯ + 2 and 𝑓(π‘₯) =
π‘₯−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(π‘₯)) π‘Žπ‘›π‘‘ 𝑔(𝑓(π‘₯))
34. 𝑓(π‘₯) = 3π‘₯ 2 + 2, 𝑔(π‘₯) = 2π‘₯
35. 𝑓(π‘₯) =
π‘₯−3
2
, 𝑔(π‘₯) = 2π‘₯ − 3
Inverse Relations and Functions
Find the inverse of each relation.
36.
37.
π‘₯
𝑦
1
0
2
1
3
0
4
2
π‘₯
𝑦
0
0
1
1
2
4
3
9
Find the inverse of each function. Is the inverse a function?
38. 𝑦 = 3π‘₯ + 1
39. 𝑦 = 2π‘₯ − 1
Graph each relation and its inverse.
41. 𝑦 = 2π‘₯ − 3
40. 𝑦 = 4 − 3π‘₯
42. 𝑦 = 3 − 7π‘₯
y
y
x
x
y
43. 𝑦 = −π‘₯
x
Download