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

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

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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.

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APPEARS IN

NCERT Class 12 Maths
Chapter 1 Relations and Functions
Q 2.3 | Page 10
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