Relations and Functions

The function f(x) = |x| has range:

1. All real numbers
2. Positive real numbers only
3. Non-negative real numbers
4. Negative real numbers

The inverse of the relation R = {(1,2), (2,3)} is:

1. {(1,2), (2,3)}
2. {(2,1), (3,2)}
3. {(3,1), (2,2)}
4. {(1,3), (2,2)}

If n(A)=4 and n(B)=3, then the number of possible functions from A to B is:

1. 7
2. 12
3. 64
4. 81

Which of the following represents an empty relation on set A?

1. A × A
2. ∅
3. {(a,a)}
4. A

If f(x) = 2x + 3, then f(4) is:

1. 8
2. 11
3. 14
4. 5

A function f: A → B is one-one if:

1. Different elements of A have different images
2. All elements of B have images
3. Every element has the same image
4. Domain is equal to range

A function f: A → B is called onto if:

1. Every element of A has an image
2. Every element of B has at least one pre-image
3. Every element of B has no image
4. A and B are equal

The range of the function f(x) = x² for x ∈ R is:

1. All real numbers
2. Non-negative real numbers
3. Negative real numbers
4. Integers only

If R = {(1,2), (2,3), (3,4)}, then the domain of R is:

1. {2,3,4}
2. {1,2,3}
3. {1,4}
4. {2,4}

If A = {1, 2, 3} and R = {(1,1), (2,2), (3,3)}, then R is:

1. Empty relation
2. Identity relation
3. Universal relation
4. Inverse relation

The domain of the function f(x) = 1/(x−2) is:

1. All real numbers
2. All real numbers except 2
3. Only positive numbers
4. Only negative numbers

If f(x) = x², then f(−3) is:

1. −9
2. 6
3. 9
4. 3

A relation R from A to B is called a function if:

1. Every element of B has one image
2. Every element of A has exactly one image in B
3. Every element of A has two images
4. No element of A has an image

If A = {1, 2} and B = {3, 4, 5}, then the number of elements in A × B is:

1. 2
2. 3
3. 5
4. 6

If A = {1, 2, 3} and B = {a, b}, then the number of relations from A to B is:

1. 5
2. 6
3. 64
4. 8