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final_exam_handout.pdf
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MATH138: College Algebra
Final Exam Handout
SHOW ALL YOUR WORK AND CLEARLY INDICATE YOUR ANSWER
1. Verify if inverse functions.
()
Verify if the functions f x =
x+5
and g ( x ) = 4x – 5 are inverses of each other.
4
2. Find the inverse function.
()
Find the inverse of the one-to-one function f x = 3×5 +1
3. Write as a single quantity and simplify.
Write the following expression as a logarithm of a single quantity, and simplify when
3
4
possible: log x + log y
5
5
4. Solve.
(
)
Solve the following equation for x: log 2 x + log 2 x – 2 = 3
5. Solve and check.
x – 2 y – 13
+
= –3
3
5
Solve the system equations and check your solution:
x + 6 y = 44
6. Minimize.
Minimize P = 19 x + 12 y subject to the following constraints:
y 2x
x 4
x 0
y 0
(Continued on next page.)
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MATH138: College Algebra
Final Exam Handout
SHOW ALL YOUR WORK AND CLEARLY INDICATE YOUR ANSWER
7. Solve.
Use Gaussian elimination method to solve the following system of linear equations:
x + 3y
= 4
−3x + 6 y + 12 z = –54
2x − 2z
= 8
8. If possible, find.
If possible, find 3A – 4B.
1 –2 –6
8 0 –5
A=
,B =
–3 1 –5
3 6 3
9. Find, if defined.
Find AC, if defined.
1 3
A = −5 2 ;
6 0
−5 1
C=
6 −8
10. Solve.
Solve the following system of linear equations using an inverse matrix:
6 x + y = 5
12 x – 5 y = –15
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