Use these set definitions and function definitions for the following exercises:
R+ = {x | x ∈ R, x ≥ 0}
H = {1, 2, 3, 4, 5}
C = {Red, Yellow, Green, Blue, Violet}
f: R+ → C
Violet if x < 450
Blue if 450 ≤ x < 495
f(x) = Green if 495 ≤ x < 570
Yellow if 570 ≤ x < 620
Red if x ≥ 620
g: C → C
c g(c)
Red Blue
Yellow Green
Green Yellow
Blue Red
Violet Yellow
h: C → H
c h(c)
Red 1
Yellow 2
Green 3
Blue 4
Violet 5
1. Is f injective? Is f surjective? Is f bijective?
For each "no" answer, if any, briefly explain why not.
2. Is g injective? Is g surjective? Is g bijective?
For each "no" answer, if any, briefly explain why not.
3. Is h injective? Is h surjective? Is h bijective?
For each "no" answer, if any, briefly explain why not.
4. Calculate the image: f([400, 500]) — that is, f({x | x ∈ R, 400 ≤ x ≤ 500}).
5. Calculate the image: g({Green, Blue, Violet}).
6. Calculate the image: h({Green, Blue, Violet}).
7. Calculate the pre-image: $f^{-1}$({Yellow, Green}). Be careful how you write the answer.
8. Calculate the pre-image: $g^{-1}$({Red, Yellow}).
9. Calculate the pre-image: $h^{-1}$({2, 3, 4}).
10. Calculate the value of $(g \circ f)(600)$. Briefly explain your answer.
11. Calculate the value of $(h \circ f)(555)$. Briefly explain your answer.
12. Write the composite function $(h \circ g)$: C → H as a table.
