Section 7.1

Simplify Radical Expressions


Multiply and Divide Radical Expressions
Rationalize the denominator
Section 7.2
Section 7.3



Add and Subtract Radical Expressions
Multiply binomial Radical Expressions
Rationalize the denominator using the conjugate
Section 7.4

Simplify expressions with rational exponents
o Write in exponential form
o Write in radical form

Solve radical equations
o With radical symbols
o With rational exponents
o With 2 radical symbols or 2 rational exponents
Section 7.5
Section 7.6


Add, subtract, multiply and divide functions
Find the composite of two functions
Section 7.7



Find domain
Find the inverse of an equation
State whether or not the inverse is a function
Study




Portfolio page
READ NOTESHEETS
Study worksheets (especially the review worksheets)
Practice problems – redo homework problems
Simplify each expression. Rationalize all denominators. Assume all variables are positive.
4
1. √81𝑥 5 𝑦 9
2. √8𝑥 3 ∙ √2𝑥 5
4. √63 + 2√28 − 5√7
5.
3.
√2𝑥 3 𝑦
√10𝑥𝑦 5
2
1+ √2
Simplify each expression. Leave all answers in exponential form.
3
6.
16𝑥 5 𝑦 10 4
(
)
81𝑥𝑦 2
1
7. (4𝑥 −2 𝑦 4 )−2
2 1
1 1
8. (𝑠 5 𝑡 3 ) (𝑠 2 𝑡 2 )
Write in exponential form.
3
9. √(2𝑥 2 )4
Solve each equation. Check for extraneous solutions.
4
10. √𝑥 + 7 = 𝑥 + 1
11. √3𝑥 − 8 = 2
12. 2(𝑥 − 1)3 = 162
14. √7𝑥 + 2 − 2 = 7𝑥
15. (−2 − 𝑥)2 − 𝑥 = 2
1
13. (2𝑥 + 1)3 = 3
1
For #16-21, let 𝑓(𝑥) = 𝑥 2 + 5 𝑎𝑛𝑑 𝑔(𝑥) = 𝑥 − 7
16. (𝑔 ° 𝑔−1 )(153)
17. 𝑔(𝑥) − 3𝑓(𝑥)
19. (𝑔 ° 𝑓)(6)
𝑓
𝑔
20. ( ) (6)
18. (𝑓 ° 𝑔)(𝑥)
21. 2𝑓(3) − 𝑔(3)
Find the domain of each function then find the inverse of each function and state whether or not the inverse is a
function.
22. 𝒇(𝒙) = √𝒙 − 𝟏 + 𝟐
23.
𝒇(𝒙) = (𝒙 + 𝟐)𝟐 − 𝟒
24. 𝒇(𝒙) = 𝟑𝒙 + 𝟐