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.
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