1. Let the functions f: R^# R^# and g: R^# R^# be defined by f(x) = 2x -3 and g(x) = x² + 5. Find f(5).

A. 7

B. 13

C. 1

D. 30

2. Let the functions f: R^# R^# and g: R^# R^# be defined by f(x) = 2x -3 and g(x) = x² + 5. Find g(-3).

A. 11

B. 2

C. 14

D. -9

3. Let the functions f: R^# R^# and g: R^# R^# be defined by f(x) = 2x -3 and g(x) = x² + 5. Find g(f(2)).

A. 1

B. 5

C. 9

D. 6

4. Let the functions f: R^# R^# and g: R^# R^# be defined by f(x) = 2x -3 and g(x) = x² + 5. Find f(g(4)).

A. 25

B. 39

C. 21

D. 5

5. Let the functions f: R^# R^# and g: R^# R^# be defined by f(x) = 2x -3 and g(x) = x² + 5. Find g(a-1).

A. a²+2a-6d

B. a²-2a-6

C. a²+2a+6

D. a²-2a+6

6. Let the functions f: R^# R^#

and g: R^# R^# be defined by f(x) = 2x -3 and g(x) = x² + 5. Find f(g(a-1)).

A. 2a²-4a-9

B. a²-4a+9

C. 2a²-4a+9

D. 2a²+4a+9

7. Let the functions f: R^# R^#
and g: R^# R^# be defined by f(x) = 2x -3 and g(x) = x² + 5. Find g(f(x)).

A. 4x²+12x-14

B. 4x²-12x-14

C. 4x²+12x+14

D. 4x²-12x+14

8. Let the functions f: R^# R^#
and g: R^# R^# be defined by f(x) = 2x -3 and g(x) = x² + 5. Find f(g(x+1)).

A. 2x²+4x+9

B. 2x²-4x+9

C. 2x²+4x-9

D. 2x²-4x-9

9. Let the functions f: R^# R^#
and g: R^# R^# be defined by f(x) = 2x -3 and g(x) = x² + 5. Find g(g(x)).

A. x³+10x² - 30

B. x⁴-10x² + 30

C. x⁴+10x² + 30

D. x²+10x + 30

10. Find f.g (composition or product) and g.f where f (x) = x2 + 1 and g(x) = x+2. Is f.g =g .f?

A. True

B. False

11. Let f (x) = ax+b and g(x) = cx+d where a, b. c, and d are constants. Determine for which constants a, b, c, and d it is true that f.g = g.f.

A. (a-1)d = (c-1)b

B. (a+d) = (c-1)b

C. ad + b = cb - d

D. ad + b = cb + d

12. Find the greatest common divisor (gcd) of 1000 and 625 by prime factorization.

A. 25

B. 130

C. 125

D. 175

13. Find the least common multiple (lcm) of 1000 and 625 by prime factorization.

A. 2000

B. 5000

C. 3000

D. 4000

14. Is the gcd(1000,625).lcm(1000,625) = 1000x625?

A. True

B. False

15. Find the gcd of 163231 and 135749 using the Euclidean algorithm.

A. 151

B. 141

C. 131

D. 121

16. Could the following table represent relations in a relational database?

Cast list
Character Actor Understudy
Hamlet Helmut Weiner John Garner, Sam Ranier
Claudius Richard Gunther Bob Searle
Ophelia Suzanne Bonner Sally Richards
Gertrude Virginia Smith No understudy

A. True

B. False

17. Form the projection (Teaching assignments) [course, instructor]

Teaching Assignments
Course Section Semester Instructor
MAT 241 1 Fall Gossett
MAT 241 2 Fall Gossett
MAT 222 1 Winter Kinney
MAT124M 1 Fall Conrath
MAT124M 2 Fall Kinney

A. course: MAT 241, MAT 241, MAT 222, MAT124M, MAT124M; instructor: Gossett, Gossett, Kinnery, Conrath, Kinney

B. course: MAT 241, MAT 222, MAT124M; instructor: Gossett, Kinnery, Conrath

C. course: MAT 241, MAT 222, MAT124M, MAT124M; instructor: Gossett, Kinnery, Conrath, Kinney