One-to-one or onto? g:Z->Z, g(n) = 3n - 2 for all n

[Brian McGee]

Hey, I'm struggling to answer the following question:

Define g : Z → Z by the rule g(n) = 3n − 2, for all integers n. Is g one-to-one and
onto? Prove or give counterexamples.

Thanks in advance.

 

[daon]

1-1: Let g(m)=g(n). Can you show m=n? i.e. start with 3m-2=3n-2.

Onto: Let k be an integer (in the codomain). Can you find an integer m (in the domain) s.t. g(m)=k?

 

[Brian McGee]

Huh?

 

[pka]

Huh?

You don't know the definitions do you?
Try to show that any linear function from R to R is one-to-one and onto.

 

[Brian McGee]

Nono I do know the definitions, I'm just confused at how to work it out. I need to see how it's done.

 

[stapel]

I need to see how it's done.

Neither your book nor your instructor worked out any examples...? That seems... unlikely.... :shock:

By the time a student is doing proofs about function properties, etc, the student is presumed to be able to figure things out by himself. Among other reasons, the student is by then well past the stage of plugging things into simplistic formulas or algorithms.

What is the definition of a "one-to-one function"? How would you go about showing that a given function fulfills this definition?

What is the definition of an "onto function"? How would you go about showing that a given function fulfills this definition?

Please reply with the definitions (word-for-word from your text and/or your class notes), along with your thoughts. Thank you!

Eliz.