Determining Onto for f: Z x Z -> Z

[lipun4u]

Determine whether f:Z x Z -> Z is onto if
1> f(m,n) = 2m-n
2> f(m,n) = |m| -|n|

 

[cristo]

You need to show some work before we can help you with your homework. What do you know about onto functions? What have you thought so far?

 

[lipun4u]

ya i kno onto function

i also know how to implement in situation like

f(x)=3x+10

but i don't know ab the above...I guess this is guanine

 

[HallsofIvy]

What is the definition of "onto" function? Do these functions satisfy the definition?
These can be done in exactly the same way as f(x)= 3x+ 10.

Well, not exactly the same- actually these are easier because you have more values to work with.

"guanine"? Isn't that one of the amino acids that make up DNA?

 

[lipun4u]

Can u please explain me how to solve it ?

 

[HallsofIvy]

You said "i also know how to implement in situation like f(x)=3x+10"

Okay, how would you determine whether that is an "onto" function?

What happens if you do exactly the same thing with f(m,n)= 2m- n?

Please show us what you would do with f(x)= 3x+ 10.

 

[lipun4u]

f(x)=y
=> 3x+10 = y
=>x=(y-10)/3

for every value of y there exists a value of x
so its an onto function