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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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