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Classify the Following Functions as Injection, Surjection Or Bijection : F : Z → Z Given By F(X) = X3

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प्रश्न

Classify the following function as injection, surjection or bijection :  f : Z → Z given by f(x) = x3

बेरीज
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उत्तर

f : Z → Z, given by f(x) = x3

Injection test:

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

f(x) = f(y)

x3 = y3

x = y

So, f is an injection.

Surjection test :

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

f(x) = y

x3 = y

x = 3sqrty  which may not be in Z.

For example, if y = 3,

x =`3 sqrt3`  is not in Z .

So, f is not a surjection and f is not a bijection .

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पाठ 2: Functions - Exercise 2.1 [पृष्ठ ३१]

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आर.डी. शर्मा Mathematics Volume 1 and 2 [English] Class 12
पाठ 2 Functions
Exercise 2.1 | Q 5.04 | पृष्ठ ३१

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