Relations and Functions Test

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Relations and Functions Test - 1

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Weekly Quiz Competition

Question 1
1 / -0

The domain of the function f (x) =

A
{x∈R:x=2nπ±π2,n∈I} {(9.PNG)} is

B
{π/2}

C
{x∈R:x=2nπ+π/2,n∈I}.

D
−ϕ

Solution

this exists only if

sinx−1≥0

sinx≥1

sinx>1,notpossible

∴sinx=1

⇒sinx=sin(2nπ+π/2)⇒x=2nπ+π/2(n∈I)
Question 2
1 / -0

If f (x) =√-x, then domain of fof is

A
(−∞,∞)

B
(−∞,0)

C
(0,∞)

D
none of these

Solution

Explanation:

√f(x) is defined only if

f(x)will be non negative.

Hence ∴√−f(x)is defined only for 0.
Question 3
1 / -0

Which of the following is/are not defined at x = 0?
a. 1/x
b. x²/x
c. x³/x
d. x³/x²

A
only a

B
b, c and d

C
a, b and c

D
all of the above
Question 4
1 / -0

The function f (x) = x + cos x

A
assumes only positive values

B
is defined for all reals

C
assumes only negative values

D
none of these

Solution

f(x)=x;g(x)=cosx

Df=R

Dg=R

D_f+g= Df∩Dg

so,

Df+g=R

SO given function is defined for all reals
Question 5
1 / -0

Which of the following is the most appropriate way to represent the equality of ordered pair?

A
(a, b) = (c, d) iff a = b = c = d

B
(a, b) = (c, d) iff a = c and b = d

C
(a, b) = (c, d) iff a = c and a = d or b = c and b = d

D
(a, b) = (c, d) iff a = c and a = d and b = c and b = d
Question 6
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 7
1 / -0

If f(x) and g(x) are two functions, then which of the following operations may increase the domain of the resulting function?

A
f(x) + g(x)

B
f(x) – g(x)

C
Both (1) and (2)

D
Neither (1) nor (2)
Question 8
1 / -0

Which of the following statements are false?
a. Every function is a relation, but every relation is not a function.
b. Every relation is a function, but every function is not a relation.
c. There is no relation between functions and relations.
d. Function is just another name of relation.

A
a, c and d

B
a, b and d

C
b, c and d

D
a, b and c

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Re-Attempt Weekly Quiz Competition

Relations and Functions Test - 1

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Relations and Functions Test - 1

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Question 1

{x∈R:x=2nπ±π2,n∈I} {(9.PNG)} is

{π/2}

{x∈R:x=2nπ+π/2,n∈I}.

−ϕ

Solution

Question 2

(−∞,∞)

(−∞,0)

(0,∞)

none of these

Solution

Question 3

only a

b, c and d

a, b and c

all of the above

Question 4

assumes only positive values

is defined for all reals

assumes only negative values

none of these

Solution

Question 5

(a, b) = (c, d) iff a = b = c = d

(a, b) = (c, d) iff a = c and b = d

(a, b) = (c, d) iff a = c and a = d or b = c and b = d

(a, b) = (c, d) iff a = c and a = d and b = c and b = d

Question 6

y ∈ I

y ∈ R, y ∈ Q.

y ∈ R

y ∈ Q

Solution

Question 7

f(x) + g(x)

f(x) – g(x)

Both (1) and (2)

Neither (1) nor (2)

Question 8

a, c and d

a, b and d

b, c and d

a, b and c

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