Math 105 assignment

MTH 105: COLLEGE ALGEBRA NAME____________________ TAKE-HOME EXAM # 3 Exam must be turned in on Monday, May 5, 2014.

ALL WORK MUST BE YOUR OWN. NO HELP SHOULD BE GIVEN. Show sufficient work for full credit.

1. Find the composition gf $ . Make sure the resulting function is simplified and in lowest terms. Also state the domain of the composite function.

� � 2 12

� �

x x

xf � � 52 4 � �

x x

xg

Find the inverse of the following functions. State the domain of � �xf 1� .

2. � � x

x xf

21 53

� �

3. � � � � 73 2 �� xxf

MTH 105: COLLEGE ALGEBRA NAME____________________ TAKE-HOME EXAM # 3 Exam must be turned in on Monday, May 5, 2014.

ALL WORK MUST BE YOUR OWN. NO HELP SHOULD BE GIVEN. Show sufficient work for full credit.

4. What is the result when a function is composed with its inverse? ______________________

5. Write the following sum and difference of logarithms as a single logarithm:

� � � � xxx 555 log12log213log3 ����

Solve the following exponential and logarithmic equations:

6. � � 124 2 eee xx � 7. 21624 2 � xx

8. 54 1 � �xe 9. 03349 ��� xx

MTH 105: COLLEGE ALGEBRA NAME____________________ TAKE-HOME EXAM # 3 Exam must be turned in on Monday, May 5, 2014.

ALL WORK MUST BE YOUR OWN. NO HELP SHOULD BE GIVEN. Show sufficient work for full credit.

10. 01222 22 �� �xx 11. 22log3 �x

12. 3536log6 � x 13. � � � � 37log1log 22 ��� xx

14. � � 29log4log2 33 ��x 15. � � 1log13log 55 �� � xx

MTH 105: COLLEGE ALGEBRA NAME____________________ TAKE-HOME EXAM # 3 Exam must be turned in on Monday, May 5, 2014.

ALL WORK MUST BE YOUR OWN. NO HELP SHOULD BE GIVEN. Show sufficient work for full credit.

16. � � � � � � � �3log2log6log1log ��� ��� xxxx

17. � � � �4ln2lnln � �� xxx

Solve the following systems of equations using substitution only.

18. 2𝑥 + 𝑦 = 5

−4𝑥 + 6𝑦 = 12 19. 3𝑥 = 24 𝑥 − 𝑦 = 4

MTH 105: COLLEGE ALGEBRA NAME____________________ TAKE-HOME EXAM # 3 Exam must be turned in on Monday, May 5, 2014.

ALL WORK MUST BE YOUR OWN. NO HELP SHOULD BE GIVEN. Show sufficient work for full credit.

Solve the following systems of equations using elimination only. Clearly define all row operations.

20. 𝑥 + 2𝑦 + 2𝑧 = 6 2𝑥 − 𝑦 + 2𝑧 = 11 4𝑥 + 5𝑦 + 𝑧 = 6

21. 3𝑥 − 𝑦 + 2𝑧 = 2 4𝑥 + 2𝑦 − 7𝑧 = 0 2𝑥 + 3𝑦 − 5𝑧 = 7

MTH 105: COLLEGE ALGEBRA NAME____________________ TAKE-HOME EXAM # 3 Exam must be turned in on Monday, May 5, 2014.

ALL WORK MUST BE YOUR OWN. NO HELP SHOULD BE GIVEN. Show sufficient work for full credit.

Solve the following systems of equations using Cramer's Rule. You must use Cramer's rule methods to obtain two of the variables; the third variable may be obtained using substitution.

22. 5𝑥 + 3𝑦 − 𝑧 = 5

3𝑥 − 2𝑦 + 4𝑧 = 13 4𝑥 + 3𝑦 + 5𝑧 = 22

23. 2𝑥 + 2𝑦 + 3𝑧 = 13 −3𝑥 + 4𝑦 − 𝑧 = 5 5𝑥 − 3𝑦 + 𝑧 = 2

MTH 105: COLLEGE ALGEBRA NAME____________________ TAKE-HOME EXAM # 3 Exam must be turned in on Monday, May 5, 2014.

ALL WORK MUST BE YOUR OWN. NO HELP SHOULD BE GIVEN. Show sufficient work for full credit.

Use the following information to evaluate the following expressions.

𝐴 = 0 3 −51 2 6 𝐵 = 4 1 0 −2 3 −2 𝐶 =

4 1 6 2 −2 3

24. (𝐴 + 𝐵)𝐶 25. 𝐴𝐶 − 3𝐼

26. Verify which matrix is the inverse of the following matrix:

𝐴 = 6 52 2 𝐴 = 2 −5 −2 6

27. Use the inverse matrix from Problem 26 to solve following system of equations:

6𝑥 + 5𝑦 = 7 2𝑥 + 2𝑦 = 2