MAT102H5 Lecture Notes - Lecture 16: Surjective Function, Bijection, Injective Function

• School: UTM
• Department: Mathematics
• Course: MAT102H5
• Professor: Alexander Rennet

Document Summary

Example: consider the following function f:a b, given by. Answer: no, for two reasons: the element g has two images, which is not allowed, the elements f and i would have no image(not allowed). xx. Definition: let a b be a function: f is injective (or one-to-one) if for each yb, there is at most one xa for which f(x)=y. If for any implies : f is surjective (or onto) if f(a)=b (i. e if every yb is the image of at least one xa under f). x = xfa x. 2 g(n) is never equal to 1. f(x) is never equal to zero. Not surjective, as f(x)>0 for all xr, so. G is not onto as g(n)2 for any nn, so. If n,nn with nn, then nnn+1n+1 g(n)g(n). x. 4)let p be the set of all non- zero polynomials (e. g ) and define f : p n{0}. f(p(x))=deg f(p(x)). F is onto, as for any nn{0} we have x.