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Check the Injectivity and Surjectivity of the Following Functions: F: Z → Z Given by F(X) = X3 - CBSE (Commerce) Class 12 - Mathematics

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Question

Check the injectivity and surjectivity of the following functions: fZ → Z given by f(x) = x3

Solution

f→ Z is given by,

f(x) = x3

It is seen that for xy ∈ Zf(x) = f(y) ⇒ x3 = y3 ⇒ x = y.

∴ f is injective.

Now, 2 ∈ Z. But, there does not exist any element x in domain Z such that f(x) = x3 = 2.

∴ f is not surjective.

Hence, function f is injective but not surjective.

  Is there an error in this question or solution?

APPEARS IN

 NCERT Solution for Mathematics Textbook for Class 12 (2018 to Current)
Chapter 1: Relations and Functions
Q: 2.5 | Page no. 10
Solution Check the Injectivity and Surjectivity of the Following Functions: F: Z → Z Given by F(X) = X3 Concept: Types of Functions.
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