Functions

1-1

Consider the function .

When x has the value of 5 the function f gives a result of 9 (2*5 -1). So, it is said that 5 is mapped to 9, i.e. the function f maps 5 to 9.

In general f maps x to 2x - 1.

The function gives one value for every number in the domain. Therefore, this function is said to be a 1-1 (one to one) mapping. A one to one mapping function is also called an injective function.

1-many

Now, consider the function .

If x, now, is given the value of 2 the function f gives a result of 6 and if x is given the value of -5 the result is 6. So, the function f maps 2 and -5 to 6.

The function gives a value for 2 different values. Therefore, this function is said to be a 1-many (one to many) mapping.

Many-1

Now, consider the function .

If x, now, is given the value of 4 the function f gives a result of ±2. The function now gives two values for every number in the domain. This is said to be a many-1 mapping.

Many-Many

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