RS Aggarwal - Mathematics

Book: RS Aggarwal - Mathematics

Chapter: 3. Functions

Subject: Maths - Class 11th

Q. No. 6 of Exercise 3F

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6

Let f : R → R : f(x) = x2 + 1. Find f–1 {10}.

Given:


f : R → R : f(x) = x2 + 1


To find inverse of f(x)


Let y = f(x)


y = x2 + 1


y-1 =


x =


f–1 (x) =


Substituting x = 10,


f–1 (10) = = = 3


Chapter Exercises

Exercise 3B
Exercise 3C
Exercise 3D
Exercise 3E
Exercise 3F
Exercise 3A

More Exercise Questions

1

Find the set of values for which the function f(x) = 1 – 3x and g(x) = 2x2 – 1 are equal.
2

Find the set of values for which the function f(x) = x + 3 and g(x) = 3x2 – 1 are equal.
3

Let X = {–1, 0, 2, 5} and f : X → R Z: f(x) = x3 + 1. Then, write f as a set of ordered pairs.
4

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5

Let f : R → R : f(x) = x2.

Determine (i) range (f) (ii) {x : f(x) = 4}
6

Let f : R → R : f(x) = x2 + 1. Find f–1 {10}.
7

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8

Let A = {6, 10, 11, 15, 12} and let f : A → N : f(n) is the highest prime factor of n. Find range (f).
9

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10

Find the range of the function f(x) = |x|.
11

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12

If then find dom (f) and range (f).
13

Let f = {(1, 6), (2, 5), (4, 3), (5, 2), (8, –1), (10, –3)} and g = {(2, 0), (3, 2), (5, 6), (7, 10), (8, 12), (10, 16)}.

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14

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15

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16

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17

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18

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19

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20

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21

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