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RD Sharma - Volume 1

Exercise 2.1

1 A 1 B 1 C 2 A 2 B 2 C 3 4 5 A 5 B 5 C 5 D 5 E 5 F 5 G 5 H 5 I 5 J 5 K 5 L 5 M 5 N 5 O 5 P 5 Q 6 7 8 A 8 B 8 C 9 A 9 B 10 11 12 13 14 15 16 17 18 19 20 21 A 21 B 21 C 22 23

Exercise 2.2

1 A 1 B 1 C 1 D 1 E 1 F 2 3 4 5 6 7 8 9 10 11 12 13 14

Exercise 2.3

1 A 1 B 1 C 1 D 1 E 1 F 1 G 1 H 1 I 2 3 4 5 6 7 8 9 10 11 A 11 B 11 C 11 D 12 13

Exercise 2.4

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Very short answer

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MCQ

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Q. 25.0( 1 Vote )

Mark the correct alternative in each of the following:

f: R → R given by is

A. injective B. surjective

C. bijective D. none of these

Class 12th RD Sharma - Volume 1 2. Functions

Answer :

Given function is f: R → R given

f(x) = x + √x²

For this function if we take x = 2,

f(x) = 2 + √4

⇒ f(x) =2

For this function if we take x = -2,

f(x) = -2 + √4

⇒ f(x) = 0

So, in general for every negative x, f(x) will be always 0. There is no x ϵ R for which f(x) ϵ (-∞, 0).

Hence, it is neither injective nor surjective and so it is not bijective either.

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PREVIOUSMark the correct alternative in each of the following:Let A = {x ϵ R : –1 ≤ x ≤ 1} = B and C = {x ϵ R : X ≥ 0} and let S = {(x, y) ϵ A × B : x2 + y2 = 1} and S0 = {(x, y) ϵ A × C : x2 + y2 = 1} Then NEXTMark the correct alternative in each of the following:If f : A → B given by 3f(x) + 2–x = 4 is a bijection, then

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