﻿ A function f: A → B, where A = {x: - 1 ≤ x ≤ 1} and B = {y: 1 ≤ y ≤ 2} is defined by the rule y = f(x) = 1 + x2 Which of the following statement is true ? | Relations and Functions

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# Relations and Functions

#### Multiple Choice Questions

11.

The number of real roots of equation loge(x) + ex = 0 is

• 0

• 1

• 2

• 3

12.

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

• 2p + q

• 2pq

• p + q

• pq

13.

Eleven apples are distributed among a girl and a boy, Then, which one of the following statements is true ?

• atleast one of them will receive 7 apples

• the girl receives atleast 4 apples or the boy receives atleast 9 apples

• the girl receives atleast 5 apples or the boy receives atleast 8 apples

• the girl receives atleast 4 apples or the boy receives atleast 8 apples

14.

The domain of definition of the function

15.

The function f(x) =  satisfies the equation

• f(x + 2) - 2f(x + 1) + f(x) = 0

• f(x) + f(x + 1) = f{x(x + 1)}

• f(x) + f(y) =

• f(x + y) = f(x)f(y)

16.

The range of the function f (x) =  is given by

17.

If , then the value of x is

• 32

• 125

• 625

• 25

18.

A mapping f : N ➔ N, where N is the set of natural numbers is defined as

f(n) = n2 for n odd

f(n) = 2n + 1, for n even

for n ∈ N. Then f is

• surjective but not injective

• injective but not surjective

• bijective

• neither injective nor surjective

# 19.A function f: A $\to$ B, where A = {x: } and B = {y: } is defined by the rule y = f(x) = 1 + x2 Which of the following statement is true ?f is injective but not surjective f is surjective but not injective f is both injective and surjective f is neither injective nor surjective

B.

f is surjective but not injective

Since, A = {x: } and B = {y: }

For x = - 1, y = 1 + (- 1)2 = 2

and for x = 1, y = 1 + 12 = 2

Thus, f is not injective.

Hence, $\forall$ of B their is preimage.

Hence, f is surjective.

20.

The equation ex - x - 1 = 0 has, apart from x = 0

• one other real root

• two real roots

• no other real root

• infinite number of real roots