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Check the Injectivity and Surjectivity of the Following Functions: F: R → R Given By F(X) = X2 - CBSE (Science) Class 12 - Mathematics

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Question

Check the injectivity and surjectivity of the given functions:  fR → R given by f(x) = x2

Solution

fR → R is given by,

f(x) = x2

It is seen that f(−1) = f(1) = 1, but −1 ≠ 1.

∴ is not injective.

Now,−2 ∈ R. But, there does not exist any element ∈ R such that f(x) = x2 = −2.

∴ f is not surjective.

Hence, function f is neither injective nor 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: 2.3 | Page no. 10
Solution Check the Injectivity and Surjectivity of the Following Functions: F: R → R Given By F(X) = X2 Concept: Types of Functions.
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