1-1 function

One-To-One Function or Injective function

A function is said to be a One-to-One Function, if for each element of range, there is a unique domain.

More About One to One Function

It satisfies both vertical line test as well as horizontal line test.
It is also Known as injective function.

Example of One to One Function

In the given figure, every element of range has unique domain.

So, the given function is one-to-one function.

                                                 Or

A function for which every element of the range of the function corresponds to exactly one element of the domain. One-to-one is often written as 1-1.

Note: y = f(x) is a function if it passes the vertical line test. It is a 1-1 function if it passes both the vertical line test and the horizontal line test. 

   Ques. is g(x)=3x-2 is a one one function?

   

   Sol:       let g(a) = g(b)

             =>  3a-2 = 3b-2

             =>  3a = 3b

             =>  a = b

            Hence g(x) is one to one function