Relations and Functions Test

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Relations and Functions Test - 3

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Weekly Quiz Competition

Question 1
1 / -0

Which of the following statements is/are true?

A
If we draw a line parallel to y-axis, then it can cut the graph of a function at a maximum of 2 points.

B
If we draw a line parallel to y-axis, then it can cut the graph of a function at a maximum of 1 point.

C
If we draw a line parallel to x-axis, then it can cut the graph of a function at a maximum of 1 point.

D
All of the above
Question 2
1 / -0

Let N be the set of natural numbers. Define a function f : N → N by f (x) = 2x + 1. Using this definition, which of the following values cannot be obtained?

A
17

B
8

C
√225

D
All of the above
Question 3
1 / -0

Which of the following statements can be used to define a function f, from a set A to set B?

a. A relation from set A to set B is said to be a function, if every element of set A has one and only one image in set B.
b. A relation from set A to set B is said to be a function, if every element of set A has a unique image in set B.
c. If, f is a function from A to B, then for a ∈ A and c, d ∈ B, then if f(a) = c and also f(b) = d, then c ≠ d.

A
a and b

B
a, b and c

C
a and c

D
only a
Question 4
1 / -0

Which of the following relations is a function?

A
R = {(x, y) : x² + y² ≤ 9} on R

B
A = {1, 2, 3}, B = {1, 2, 3, 4, 5} and R = {(x, y) : 5x + 2y} is a prime number on A .

C
A = {(1, 2, 3}, B = {1, 2, 3, 4, 5, 6, 7} and R = {(x, y) | y =x² – 3x + 3} on A

D
None of these
Question 5
1 / -0

Let x be any real, then [x + y] = [x] + [y] holds for

A
y ∈ I

B
y ∈ R, y ∈ Q.

C
y ∈ R

D
y ∈ Q

Solution

[x]=x ∀ x∈I

so,

[x+y]=[x]+[y] only if x and y ∈ I
Question 6
1 / -0

Let f(x) = 1/1-x, then (fofof) (x) equals to

A
x

B
1/1-3x

C
x/1-3x

D
None of these
Question 7
1 / -0

If f (x) =√−x, then domain of fof is

A
(−∞,∞)

B
(−∞,0)

C
(0,∞)

D
none of these

Solution

√f(x) is defined only if

f(x)will be non negative.

Hence ∴√−f(x is defined only for 0.

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Relations and Functions Test - 3

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Relations and Functions Test - 3

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Question 1

If we draw a line parallel to y-axis, then it can cut the graph of a function at a maximum of 2 points.

If we draw a line parallel to y-axis, then it can cut the graph of a function at a maximum of 1 point.

If we draw a line parallel to x-axis, then it can cut the graph of a function at a maximum of 1 point.

All of the above

Question 2

17

8

√225

All of the above

Question 3

a and b

a, b and c

a and c

only a

Question 4

R = {(x, y) : x2 + y2 ≤ 9} on R

A = {1, 2, 3}, B = {1, 2, 3, 4, 5} and R = {(x, y) : 5x + 2y} is a prime number on A .

A = {(1, 2, 3}, B = {1, 2, 3, 4, 5, 6, 7} and R = {(x, y) | y =x2 – 3x + 3} on A

None of these

Question 5

y ∈ I

y ∈ R, y ∈ Q.

y ∈ R

y ∈ Q

Solution

Question 6

x

1/1-3x

x/1-3x

None of these

Question 7

(−∞,∞)

(−∞,0)

(0,∞)

none of these

Solution

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R = {(x, y) : x² + y² ≤ 9} on R

A = {(1, 2, 3}, B = {1, 2, 3, 4, 5, 6, 7} and R = {(x, y) | y =x² – 3x + 3} on A