State whether the following functions are well-defined. If they are, then give the Domain, Co-domain and Range and state whether the functions are one-to-one and/or onto and give your reasoning. If they are not well defined, then explain why not.
a) f: J → J, f(x) = 3x + 1
b) g: N → N, g(x) = x2 – 1
c) h: N → R, h(x) = +x
d) j: {words} → {letters}, j(x) = initial letter of x
I will appreciate if someone gives correct answers to each part. Thanks
This looks like homework, so I'll just guide you through the las problem and see if you can do the rest on your own.
d) j: {words} → {letters}, j(x) = initial letter of x
Domain: words Co-Domain: letters Range: letters
Is this onto? Because there is at least one word that starts with each letter, you can get all possible values in the Co-Domain, so it is onto.
Is this one-to-one? Well, no. For example, apple and alligator will give the same return value even though they are different words.