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