# Mathematics

Content type
User Generated
Subject
Mathematics
School
Virginia State University
Type
Homework
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1
Mathematics Quiz
Name
Institution
Course
Date

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2
Problem
Number
Solution
1
Work:   

 

   
  
   
   
   
2



Work:


Let y be h(x)
Therefore,



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1 Mathematics Quiz Name Institution Course Date 2 Answer Sheet Record your answers and work. Problem Solution Number 1 Answer: 𝑥 = 2, 2 Work: (4𝑥 − 5)4 = 81 4 √(4𝑥 − 5)4 = ∜81 4𝑥 − 5 = ±3 4𝑥 − 5 = 3 4𝑥 = 3 + 5 𝑥= 8 4 1 𝒙=𝟐 4𝑥 − 5 = −3 4𝑥 = −3 + 5 𝑥= 2 4 𝒙= 𝟏 𝟐 𝑥+3 Answers:ℎ−1 (𝑥) = 𝑥+2 Work:ℎ(𝑥) = 2 2𝑥−3 1−𝑥 Let y be h(x) Therefore, 𝑦 = 2𝑥−3 1−𝑥 3 Then swap x with y, and solve the resulting equation for x in order to find the inverse swapping the variables; 𝑦 = Solving the equation 𝑥 = 2𝑥−3 1−𝑥 2𝑦−3 1−𝑦 becomes, 𝑥 = 2𝑦−3 1−𝑦 for y 𝑦= 𝑥+3 𝑥+2 Answer: 𝑥 = −3 Work:(1 − 𝑥)3/2 = 8 Squaring both sides to remove the root (1 − 𝑥)3 = 64 3 Finding the cube root on both sides 1−𝑥 =4 −𝑥 = 4 − 1 𝑥 = -3 4 4 Answer: 𝐹𝑢𝑛𝑐𝑡𝑖𝑜𝑛 𝑑𝑜𝑚𝑎𝑖𝑛: 𝑥 < 3 , 𝐼𝑛𝑡𝑒𝑟𝑣𝑎𝑙 𝑁𝑜𝑡𝑎𝑡𝑖𝑜𝑛: (−∞, 3) Work: 4 − 3𝑥 > 0 4 −3𝑥 > 0 − 4 −3𝑥 > −4 3𝑥 < 4 𝑥< 4 3 4 1 Answers: 3 Work:log 8 2 Let log82 be x log 8 2 = 𝑥 5 Expressing in index form 8𝑥 = 2 23(𝑥) = 21 3𝑥 = 1 𝑥= 1 3 Answer: No solution Work: √𝑥 + √7𝑥 + 2 = 0 √𝑥 = −√(7𝑥 + 2) (√𝑥)2 = (−√7𝑥 + 2)2 Apply exponents rule (−𝑎)𝑛 = 𝑎2 𝑥 = 7𝑥 + 2 6 𝑥 − 7𝑥 = 2 −6𝑥 = 2 𝑥 ...
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