Ex 1.2
You are here
Last updated at Dec. 16, 2024 by Teachoo
Something went wrong!
The
video
couldn't load due to a technical hiccup.
But don't worry — our team is already on it, and we're working hard to get it back up ASAP.
Thanks for bearing with us!
Transcript
Ex 1.2, 2 Check the injectivity and surjectivity of the following functions: (i) f: N → N given by f(x) = x2 f(x) = x2 Checking one-one (injective) f (x1) = (x1)2 f (x2) = (x2)2 Putting f (x1) = f (x2) (x1)2 = (x2)2 ∴ x1 = x2 or x1 = –x2 Since x1 & x2 are natural numbers, they are always positive. Hence, x1 = x2 Hence, it is one-one (injective) Check onto (surjective) f(x) = x2 Let f(x) = y , such that y ∈ N x2 = y x = ±√𝒚 Putting y = 2 x = √2 = 1.41 Since x is not a natural number Given function f is not onto So, f is not onto (not surjective)
