Sets, Relations and Functions Test

Result

Sets, Relations and Functions Test - 14

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Weekly Quiz Competition

Question 1
4 / -1

If f(x)• f(1/x) = f(x) + f(1/ x) and f(4) = 65,then f(6) is equal to

A
65

B
217

C
215

D
64

Solution
Question 2
4 / -1

If f(x) = ax + b, g(x) = cx + d, then f{g(x)} = g {f(x)} is equivalent to

A
f(a) = g(c)

B
f(b) = g(b)

C
f(d) = g(b)

D
f(c) = g(a)

Solution
Question 3
4 / -1

If Q denotes the set of all rational numbers and f (p/q) = √p² - √q² for any p/q ϵ Q, then observe the following statements.
I. f(p/q) is real for each p/q ϵ Q
II. f(p/q) is a complex number for each p/q ϵ Q

A
Both I and II are correct

B
I is correct, II is incorrect

C
I is incorrect, II is correct

D
Both I and II are incorrect

Solution
Question 4
4 / -1

If f : R → R is given by

A
1

B
-1

C
√3

D
0

Solution
Question 5
4 / -1

If f(x) = (a-xⁿ)^1/n , where a > 0 and n ϵ N, then fof(x) is equal to

A
a

B
x

C
xⁿ

D
aⁿ

Solution
Question 6
4 / -1

If f : (2, 3) → (0,1) is defined by f(x) = x - [x] , then f^-1(x) is equal to

A
x - 2

B
x + 1

C
x - 1

D
x + 2

Solution
Question 7
4 / -1

A
(1, 4)

B
[1, 4)

C
(1, 4]

D
[1, 4]

Solution
Question 8
4 / -1

If X = {4ⁿ - 3n - 1: n ∈ N} and Y = {9(n - 1): n ∈ N}, where N is the set of natural numbers, then X ∪ Y is equal to

A
N

B
Y - X

C
X

D
Y

Solution
Question 9
4 / -1

The set A = {x : |2x + 3| < 7} is equal to the set

A
D = { x : 0 < x+5 < 7 }

B
B = { x : -3 < x < 7 }

C
E = { x : -7 < x < 7 }

D
C = { x : -13 < 2x < 4 }

Solution
Question 10
4 / -1

If the number of elements of the sets A and B are p and q, respectively. Then, the number of relations from the set A to the set B is

A
2^p+q

B
2^pq

C
p+q

D
pq

Solution