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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

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Very short answer

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MCQ

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Q. 175.0( 3 Votes )

If f: R → (–1, 1) defined by is invertible, find f^-1.

Class 12th RD Sharma - Volume 1 2. Functions

Answer :

We have f: R → (–1, 1) and

Given that f^-1 exists.

Let y ϵ (–1, 1) such that f(x) = y

⇒ 10^2x – 1 = y (10^2x + 1)

⇒ 10^2x – 1 = 10^2xy + y

⇒ 10^2x – 10^2xy = 1 + y

⇒ 10^2x (1 – y) = 1 + y

Taking log₁₀ on both sides, we get

We have f(x) = y ⇒ x = f^-1(y)

But, we found f(x) = y ⇒

Hence,

Thus,

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PREVIOUSLet f : R – → R be a function defined as. Show that f : R – → range(f) is one-one and onto. Hence, find f-1.NEXTIf f: R → (0, 2) defined by is invertible, find f-1.

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