# Relations And Functions

15 Questions | Total Attempts: 1711  Settings  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 = {(1, 2), (3, 5), (4, 1)} and = {(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.
• 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.
• 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 .
• A.
• B.
• C.
• D.
• 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 = {(xy): 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 = {(xy): 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.
• 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’?
• 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.
• A.
• B.
• C.
• D.
• 15.
Let A = N X N and * be the binary operation on A defined by (ab)*(cd) = (cd) What is true about ‘*’
• A.

Commutative

• B.

Associative

• C.

Commutative and associative

• D.

None of these

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