Question 5 For the following two functions, which of the following is correct: f(x)=x4+1 from the set of all real numbers to itself, g(x)={ (1,1), (2,3), (3,2)} from the set {1,2,3} to itself? A) both are one-to-one B) the first, but not the second, is one-to-one C) the second, but not the first, is one-to-one D) neither is one-to-one
For the following two functions, which of the following is correct: f(x)=x4+1 from the set of all real numbers to itself, g(x)={ (1,1), (2,3), (3,2)} from the set {1,2,3} to itself?
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A) both are one-to-one
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B) the first, but not the second, is one-to-one
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C) the second, but not the first, is one-to-one
- D) neither is one-to-one
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A) both are onto
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B) the first, but not the second, is onto
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C) the second, but not the first, is onto
- D) neither is onto
Which of the following is always true of composition of functions, whether are not they are one-to-one or onto?
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A) it is associative
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B) it is commutative
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C) it is constant
- D) the composition is invertible
Compute the composition (product) of these two permutations
| ( | 1 | 2 | 3 | 4 | 5 | 6 | ) |
| ( | 3 | 5 | 4 | 1 | 2 | 6 | ) |
,
| ( | 1 | 2 | 3 | 4 | 5 | 6 | ) |
| ( | 2 | 4 | 5 | 3 | 1 | 6 | ) |
Is it, in some order (we use the order of the book)
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A)
( 1 2 3 4 5 6 ) ( 1 2 3 4 5 6 ) -
B)
( 1 2 3 4 5 6 ) ( 5 1 2 4 3 6 ) -
C)
( 1 2 3 4 5 6 ) ( 6 1 2 4 3 5 )
- D)
| ( | 1 | 2 | 3 | 4 | 5 | 6 | ) |
| ( | 2 | 4 | 5 | 3 | 1 | 6 | ) |
Suppose a square is represented with these 4 vertices in order: A is (1,1), B is (1,-1), C is (-1,-1), D is (-1,1). Note that these go clockwise around the square. Which of the following is a valid symmetry and a valid classification of that symmetry?
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A) A,B,C,D in order go to B,C,D,A a rotation by 90 degrees
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B) A,B,C,D in order go to D,C,A,B a reflection
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C) A,B,C,D in order go to D,C,B,A a rotation by 90 degrees
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D) A,B,C,D in order go to A,B,D,C a reflection
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