MATH107 University of Maryland University Simplifying Expressions Quiz 5

Need to make sure my solutions are right. Anytime I solve on my own I make mistakes and my grades keep going down.

Math 107 Quiz 5
Professor: Dr. Kamal Hennayake
Name________________________________
Instructions:
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The quiz is worth 50 points. There are 10 problems, each worth 5 points. Your score on the quiz will be
converted to a percentage and posted in your assignment folder with comments.
This quiz is open book and open notes, and you may take as long as you like on it provided that you
submit the quiz no later than the due date posted in our course schedule of the syllabus. You may refer
to your textbook, notes, and online classroom materials, but you may not consult anyone.
You must show all of your work to receive full credit. If a problem does not seem to require work, write
a sentence or two to justify your answer.
Please type your work in your copy of the quiz, or if you prefer, create a document containing your
work. Scanned work is also acceptable. Be sure to include your name in the document. Review
instructions for submitting your quiz in the Quizzes Module.
If you have any questions, please contact me by e-mail (kamal.hennayake@faculty.umuc.edu).
At the end of your quiz you must include the following dated statement with your name typed in lieu of
a signature. Without this signed statement you will receive a zero.
I have completed this quiz myself, working independently and not consulting anyone except the instructor. I
have neither given nor received help on this quiz.
Name:
Date:
Please remember to show ALL of your work on every problem. Read the basic rules for
showing work below BEFORE you start working on the quiz.
a) Each step should show the complete expression or equation rather than a piece of it.
b) Each new step should follow logically from the previous step, following rules of algebra.
c) Each new step should be beneath the previous step.
d) The equal sign, =, should only connect equal numbers or expressions.
If you have questions about showing work, please ask.
Math 107
Quiz 5
Page 2
Did you read the rules for showing work on page 1 of the quiz? If not, please go back to page 1 now and
read them. If you do not show work correctly, you will not earn full credit.
1) Use the given pair of functions to find the following values if they exists. Show work neatly.
(a) (𝑓 ∘ 𝑔)(1)
5
𝑓(𝑥) = 𝑥 − 4, 𝑎𝑛𝑑 𝑔(𝑥) = 5𝑥 2 + 3𝑥 + 4
6
(b) (𝑔 ∘ 𝑓)(6)
(c) (𝑓 ∘ 𝑔)(−1)
6
(d) (𝑓 ∘ 𝑓) (5)
(e) (𝑔 ∘ 𝑔)(0)
2) Use the given pair of functions to find and simplify expressions for the following functions. State the domain
of each using interval notation.
𝑓(𝑥) =
(a) (𝑔 ∘ 𝑓)(𝑥)
(b) (𝑓 ∘ 𝑔)(𝑥)
1
4
𝑎𝑛𝑑 𝑔(𝑥) = + 2
𝑥−2
𝑥
Math 107
Quiz 5
Page 3
3) Consider the function 𝑓(𝑥) = √4 − 𝑥 = 2. Show work clearly for credit.
(a) Find the inverse of the function.
(b) Find the domain and range of the inverse function. State the domain and range using interval notation.
1
4) Consider the function 𝑓(𝑥) = 𝑥+11. Show work clearly for credit.
(a) Show it is one-to-one algebraically.
(b) Find its inverse of the function.
Math 107
Quiz 5
Page 4
5) Find the inverse of the function 𝑓(𝑥) = 2𝑥 − 1. Draw the functions 𝑓 and 𝑓 −1 .
6) Rewrite the following equations in the other form. That is, rewrite the exponential equations as logarithmic
equations and rewrite the logarithmic equations as exponential.
(a) 𝑒 𝑡 = 11
(b) log 1000 = 3
(c) 43 = 64
(d) 10−2 = 0.01
(e) ln 𝑓 = 𝑏
Math 107
Quiz 5
Page 5
7) Evaluate the expression. Show work or give a justification. Do not use a calculator and give decimal
approximation. Give the exact answers only.
1
(a) log 25 (125)
(b) log 9 (243)
(c) log 9 √243
(d) log 9 (
1
)
√243
(e) log 2 √2
8) Solve the following equations. Show work or give a justification.
(a) 𝑏 5 = 243
(b) 28 ∙ 𝑏 4 − 76 = 17426
1
(c) 53𝑛−4 = 125
(d) 3(2𝑥+5)(2𝑥+1) = 1
(e) 𝑒 2𝑘+4 = 𝑒 2
Math 107
Quiz 5
Page 6
Consider the following data set for #9 and #10.
9) Use exponential regression to find an exponential function that best fits this data.
10) Use linear regression to find a linear function that best fits this data.
Of these two functions (#9 and #10) which equation best fits the data. Justify your answer or show work or
graphs.
End of quiz: please remember to sign and date the honor statement in the box on the first page of the quiz.