Honors Algebra 2
6.1 – 6.2 Review Worksheet
Name:
Period:
𝒇
Find (𝒇 + 𝒈)(𝒙), (𝒇 − 𝒈)(𝒙), (𝒇 ∙ 𝒈)(𝒙), (𝒈) (𝒙) and state the domain of each resulting function.
1. Given f(x) = 4𝑥2 and g(x) =
1
𝑥3
,
2. Given f(x) = 𝑥 2 + 3x – 4 and g(x) = x – 1
(𝒇 + 𝒈)(𝒙) =
(𝒇 + 𝒈)(𝒙) =
(𝒇 − 𝒈)(𝒙) =
(𝒇 − 𝒈)(𝒙) =
(𝒇 ∙ 𝒈)(𝒙) =
(𝒇 ∙ 𝒈)(𝒙) =
𝒇
𝒇
(𝒈) (𝒙) =
(𝒈) (𝒙) =
Find (𝒇 ∘ 𝒈)(𝒙) and (𝒈 ∘ 𝒇)(𝒙).
3. Given 𝑓(𝑥) = 𝑥 2 + 3𝑥 − 2 and 𝑔(𝑥) = 3𝑥 − 4.
4. 𝑓(𝑥) = 𝑥 + 2 and 𝑔(𝑥) = 𝑥 2 − 4
Find the inverse of the given function.
2
5. 𝑓(𝑥) = − 3 𝑥 − 4.
6.
x
-3
2
5
8
f(x)
-9
1
7
13
Determine whether the given functions are inverses. Explain why or why not.
7.
8.
x
f(x)
x
g(x)
1
2
2
1
0
-3
-3
0
-5
-4
-4
-5
7
7
7
7
9.
𝑓(𝑥) = 2𝑥 − 1
𝑔(𝑥) = 2𝑥 + 1
10. A group of engineers is designing a staple gun. One team determines that the speed of impact s of the staple (in feet
per second) as a function of the handle length ℓ (in inches) is given by s(ℓ) = 40 + 3ℓ. A second team determines that
𝑠 −10
the number of sheets N that can be stapled as a function of the impact speed is given by N(s) = 3 . What function
gives N as a function of ℓ?
11. The Clearys are replacing the flooring in their 15 foot by 18 foot kitchen. The new flooring costs $17.99 per square
yard. The formula f(x) = 9x converts square yards to square feet.
a. Find the inverse 𝑓 −1(x). What is the significance of 𝑓 −1(x) for the Clearys?
b. What will the new flooring cost the Clearys?
4
12. Jason wants to make a spherical water cooler that can hold half a cubic meter of water. He knows that V = 3 π𝑟 3 , but
he needs to know how to find r given V. Find this inverse function.