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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