Math 112 Final Exam 12 pts each May 4, 2004

Solve for x.

1.

2. mx - ay = 2x + c(x - 1)

3. | 4x + 2 | < 4

4. x^2/3 - x^1/3 - 12 = 0

5. Solve the linear inequality. Leave the answer in inequality notation.

3x - 2 ≤ 4(x + 2) - 5

6. Solve the system of equations

2x - y = 16

x + 3y = 1

7. Find the domain of the function.

8. Given the two points (-2, -3) and ( -1, 5):

a. Find the distance between them.

b. Find the slope of the line between them.

c. Find the equation of the line passing thru them.

d. Graph the line.

9. Given f(x) = x² - 4:

Find f(2), f(a²), f(2b), f(2+b)

10. Given f(x) = -2x² - 12 x + 15: Sketch, and find vertex, axis of symmetry, and maximum or minimum value of the function.

11. Given f(x) = , find f ^-1(x)

12. Graph and give domain and range for :

a. y = (1/4)^x

b. y = log₂

13. Find x:

a. log_x16 = 4

b. log₅ x = 3

c. log₅ 0 = x

14. a. Use the laws of logs to expand:

b. Use the laws of logs to contract:

log₂ 4 + log₂ 5 - log₂ 8 - log₂ 10

Solve for x.

15. 4 ^{2x + 1}= 7^{2x - 1}

16. log₂(x + 1) + log₂(x - 1) = 3