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check the injectivity and surjectivity f:N_N given by f(x)=x**2

Posted by Siddhu Sravan 4 years, 4 months ago

CBSE > Class 12 > Mathematics

1 answers

Mishti ???? 4 years, 4 months ago

Solution~~ f : N → N given by f (x) = x² We can see that for x, y ϵ N, f(x) = f(y) ⇒ x² = y² ⇒ x = y ⇒ f is injective. Now, let 2 ϵ N. But, we can see that there does not exists any x in N such that f(x) = x² = 2, therefore, f is not surjective. Therefore, function f is injective but not surjective. Regards. ??

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