Week 12

I've used onto and 1-1 (surjective and injective) in linear algebra when looking at isomorphisms. We looked at a number of bijective transformations in class but didn't really analyze some examples that do not fall into that category. How about the following:

f(x) = |x| will cause both x = +1 and x = -1 to yield f(x) = 1 so it won't be 1-1. Secondly, nothing yields -1 so it's not onto either.

f(x) = sqrt(x) is the opposite of the previous example. Instead of taking 2 numbers and giving the same number, it spits out 2 different numbers from the input of only 1. Say x = 1, then f(x) = -1 and 1.

I think these are the simplest examples I can think of.