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Let A = [-1, 1]. Then, Discuss Whether the Following Functions From A To Itself Are One-one, Onto Or Bijective : `F (X) = X/2` - Mathematics

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Question

Let A = [-1, 1]. Then, discuss whether the following function from A to itself is one-one, onto or bijective : `f (x) = x/2`

Sum
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Solution

`f : A → A, given  by  f (x) = x/2 `

Injection test :

Let x and y be any two elements in the domain (A), such that f(x) = f(y).

f(x) = f(y)

`x/2 = y /2`

x = y

So, f is one-one.

Surjection test :

Let y be any element in the co-domain (A), such that f(x) = y for some element x in A(domain)

f(x) = y

`x/2 = y`

x = 2y, which may not be in A.

For example, if y = 1, then

x = 2, which is not in A.

So, f is not onto.

So, f is not bijective.

 

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Chapter 2: Functions - Exercise 2.1 [Page 32]

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RD Sharma Mathematics [English] Class 12
Chapter 2 Functions
Exercise 2.1 | Q 8.1 | Page 32

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