One-to-One Functions

[nycmathguy]

What is the most basic definition of a one-to-one function? Can you provide an example? To my knowledge, a one-to-one function is easily spotted when the y-coordinate is repeated? If the x-coordinate is repeated, there is no function.

You say?

 

[MathLover1]

One to one functions are special functions that return a unique range for each element in their domain i.e, the answers never repeat.

As an example the function
g(x) = x - 4
is a one to one function since it produces a different answer for every input.

Also, the function g(x) = x^2 is not a one to one function since it produces 4 as the answer when the inputs are 2 and -2. A function that is not a one to one is called a many to one function.

 

[nycmathguy]

One to one functions are special functions that return a unique range for each element in their domain i.e, the answers never repeat.

As an example the function
g(x) = x - 4
is a one to one function since it produces a different answer for every input.

Also, the function g(x) = x^2 is not a one to one function since it produces 4 as the answer when the inputs are 2 and -2. A function that is not a one to one is called a many to one function.

So far so good.