Relations And Functions
.JPG "Relations And Functions")
Time: 30 Minute
- 1.If f: R →R is defined by f(x) = 3x + 2, define f [f(x)].
- A.
9x+5
- B.
9x+8
- C.
9x+4
- D.
9x-4
- 2.Let f: {1, 3, 4} → {1, 2, 5} and g: {1, 2, 5} → {1, 3} be given by f = {(1, 2), (3, 5), (4, 1)} and g = {(1, 3), (2, 3), (5, 1)}. What will be the value of gof.
- A.
Gof = {(1, 3), (3, 1), (4, 3)}
- B.
Gof = {(1, 3), (3, 1), (2, 3)}
- C.
Gof = {(2, 3), (3, 1), (4, 3)}
- D.
Gof = {(1, 3), (3, 4), (4, 3)}
- 3.
![- ProProfs]()
- A.
F is invertible
- B.
F is not invertible
- C.
None of the above
- D.
Both A & B
- 4.For the relation R in the set {1, 2, 3} given by R = {(1, 2), (2, 1)), what is true about R?
- A.
R is reflexive
- B.
R is transitive
- C.
Neither A nor B
- D.
Both A & B
- 5.
![- ProProfs]()
- A.
One-one
- B.
Onto
- C.
Neither A nor B
- D.
None of these
- 6.What is true regarding the given function? f: R → R defined by f(x) = 3 − 4x
- A.
Onto
- B.
Bijective
- C.
Neither A nor B
- D.
Both A & B
- 7.
![The function f in defined as is one-one and onto. Find . - ProProfs]( "The function f in defined as is one-one and onto. Find .")
The function f in defined as is one-one and onto. Find .- A.
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- B.
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- C.
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- D.
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- 8.Consider f: R → R given by f(x) = 4x + 3. Find weather f is invertible. Find the inverse of f.
- A.
Not invertible, (y – 3 / 4)
- B.
Invertible, (y – 3 / 4)
- C.
Not invertible, (y + 3 / 4)
- D.
Invertible, (y + 3 / 4)
- 9.What is true regarding the given function? Relation R in the set A = {1, 2, 3…13, 14} defined as R = {(x, y): 3x − y = 0}
- A.
Reflexive
- B.
Symmetric
- C.
Transitive
- D.
None of the above
- 10.What is true regarding the given function? Relation R in the set N of natural numbers defined as R = {(x, y): y = x + 5 and x < 4}
- A.
Reflexive & symmetric
- B.
Symmetric & transitive
- C.
Both A & B
- D.
None of the above
- 11.What is true regarding the given functions? 1. f: N → N given by f(x) = x2 2. f: Z → Z given by f(x) = x2
- A.
Both functions are not injective
- B.
Both functions are not subjective
- C.
Both functions are not subjective
- D.
Both functions are injective
- 12.
![- ProProfs]()
- A.
Bijective
- B.
Not bijective
- C.
Onto
- D.
Both B & C
- 13.
![Let A = R − {3} and B = R − {1}. Consider the function f: A → B defined by . What is true about ‘f’? - ProProfs]( "Let A = R − {3} and B = R − {1}. Consider the function f: A → B defined by . What is true about ‘f’?")
Let A = R − {3} and B = R − {1}. Consider the function f: A → B defined by . What is true about ‘f’?- A.
One-one
- B.
Onto
- C.
One-one and onto
- D.
None of these
- 14.
![The function f: [−1, 1] → R, given by is one-one. Find the inverse of the function f: [−1, 1] → Range f. - ProProfs]( "The function f: [−1, 1] → R, given by is one-one. Find the inverse of the function f: [−1, 1] → Range f.")
The function f: [−1, 1] → R, given by is one-one. Find the inverse of the function f: [−1, 1] → Range f.- A.
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- B.
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- C.
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- D.
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- 15.Let A = N X N and * be the binary operation on A defined by (a, b)*(c, d) = (a + c, b + d) What is true about ‘*’
- A.
Commutative
- B.
Associative
- C.
Commutative and associative
- D.
None of these
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.JPG)
![The function f: [−1, 1] → R, given by is one-one. Find the inverse of the function f: [−1, 1] → Range f. - ProProfs](/api/ckeditor3.6.9/plugins/ckeditor_wiris/integration/showimage.php?formula=a06b62a618d4b000bab8e2146f2f9290.png "The function f: [−1, 1] → R, given by is one-one. Find the inverse of the function f: [−1, 1] → Range f.")
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