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

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

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 129 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45

MCQ

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55

Q. 185.0( 1 Vote )

If f: R → (0, 2) defined by is invertible, find f^-1.

Class 12th RD Sharma - Volume 1 2. Functions

Answer :

We have f: R → (0, 2) and

Given that f^-1 exists.

Let y ϵ (0, 2) such that f(x) = y

⇒ 2e^2x = y (e^2x + 1)

⇒ 2e^2x = e^2xy + y

⇒ 2e^2x – e^2xy = y

⇒ e^2x (2 – y) = y

Taking ln on both sides, we get

We have f(x) = y ⇒ x = f^-1(y)

But, we found f(x) = y ⇒

Hence,

Thus,

Rate this question :

How useful is this solution?

We strive to provide quality solutions. Please rate us to serve you better.

PREVIOUSIf f: R → (–1, 1) defined by is invertible, find f-1.NEXTLet f : [–1, ∞) → [–1, ∞) is given by f(x) = (x + 1)2 – 1. Show that f is invertible. Also, find the set S = {x: f(x) = f-1(x)}

Related Videos

Functions - 01

Functions - 01

Functions - 0152 mins

Functions - 10

Functions - 10

Functions - 1047 mins

Functions - 05

Functions - 05

Functions - 0558 mins

Functions - 07

Functions - 07

Functions - 0748 mins

Inverse Trigonometric Functions - 01

Inverse Trigonometric Functions - 01

Inverse Trigonometric Functions - 0161 mins

Range of Functions

Range of Functions

Range of Functions58 mins

Functions - 02

Functions - 02

Functions - 0253 mins

Functions - 03

Functions - 03

Functions - 0361 mins

Functions - 08

Functions - 08

Functions - 0840 mins

Functions - 12

Functions - 12

Functions - 1252 mins

Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts

Dedicated counsellor for each student

24X7 Doubt Resolution

Daily Report Card

Detailed Performance Evaluation

caricature

view all courses

RELATED QUESTIONS :

Let f :R → R be given by f (x) = tan x. Then f^–1 (1) is

Mathematics - Exemplar

| Let * be a binary operation on Q defined by

Show that * is commutative as well as associative. Also find its identity elements, if it exists.

Mathematics - Board Papers

Find the identity element in the set Q + of all positive rational numbers for the operation * defined by for all a, b ∈ Q +.

Mathematics - Board Papers

Let f : A → B and g : B → C be the bijective functions. Then (g o f)^–1 is

Mathematics - Exemplar

Show that the binary operation * on defined as for all is commutative and associative on A. Also find the identify element of * in A and prove that every element of A is invertible.

Mathematics - Board Papers

Determine whether each of the following operations define a binary operation on the given set or not:

‘*’ on Q defined by for all a,b Q.

RD Sharma - Volume 1