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

ID: 3862877 • Letter: 1

Question

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

Explanation / Answer

I am here providing you the answer for first 4 questions

1.) f(5) = 2*5 - 3 = 10-3 = 7

2.) g(-3) = (-3)^2 + 5 = 9+5 = 14

3.) f(2) = 2*2 - 3 = 1

g(f(2)) = g(1) = 1^2 + 5 = 6

4.) g(4) = 4^2 + 5 = 16+5 = 21

f(g(4)) = f(21) = 2*21 - 3 =42-3 = 39

Hope it helps, do give your response.