Functions

[fg9]

I'm trying to understand the concept of "1-1" and "onto" functions.
Here is an example:
The function f(x)= x/2 (when x is even) and 0 (when x is odd).
Would it be fair to say there are no points of intersection/similarity between the two types.
Does this make it a "1-1" thing (and not an "onto")?

 

[Dr.Peterson]

I'm trying to understand the concept of "1-1" and "onto" functions.
Here is an example:
The function f(x)= x/2 (when x is even) and 0 (when x is odd).
Would it be fair to say there are no points of intersection/similarity between the two types.
Does this make it a "1-1" thing (and not an "onto")?

Are you taking the domain to be integers, since non-integers are neither even not odd?

What do you mean by "no points of intersection/similarity between the two types"? Give some examples of what you mean.

This is a function (from the integers to the integers) because every integer is even or odd; it is not one-to-one because all odd numbers map to the same value, 0. It is "onto" because every integer is half of some (even) integer. So your statement is exactly backward.

 

[Steven G]

A function f(x) is said to be 1-1 if whenever f(a) = f(b) then it follows that a=b.

Example 1: Is f(x) = 3x-5 1-1?
Suppose f(a) = f(b)
Then 3a-5 = 3b-5
Then 3a = 3b
Then a=b. So f(x) is 1-1

Example 2: Is f(x) = x^2 1-1?
Suppose f(a) = f(b)
Then a^2 = b^2
Then a = +/- b
So f(x) is NOT 1-1 (since a does NOT have to equal b)

 

[Steven G]

I'm trying to understand the concept of "1-1" and "onto" functions.
Here is an example:
The function f(x)= x/2 (when x is even) and 0 (when x is odd).
Would it be fair to say there are no points of intersection/similarity between the two types.

No, it would not be fair to say that there are no points of intersection. Suppose x = 0, which is even. So f(0) = 0/2 = 0. Now f(any odd number) = 0. So there is an intersection between the two types.

Before you can talk about onto you have to state a set that you want to know if the function is onto.

 

[fg9]

Much appreciated!