• A special type of Relation where each input value maps to exactly one output value. In relation, we can have one element is a parent of one or more other elements. But in function, we have one element is a square of another element


Each element in the Domain maps to a distinct element in the Co-domain.


Every element in the codomain is covered by the function. However, the function shown in the diagram below isn’t injective, since 2 inputs point to the same output.


When a function is both injective & surjective. When a function has a Inverse Function, we can say it is bijective. Since inverse function uses the codomain of the original function as domain - surjective & inverse function follows the rule of function, each input maps to exactly one output - this shows no input value from the original function maps to more than one output, thus injective.


The same input always produces the same output.

Referential Transparency

The output depends only on the input.

Inverse Function


Given , then .

If , then , .

Visual relationship with function

Inverse function is basically a reflection of the original function about the line

Real-value function

Polynomial Function

  • is constant, and the polynomial function above is called polynomial of degree


A polynomial of degree can be factored as a product of linear and quadratic Factor.

For example, , where and are linear factors and is quadratic factor.

Rational Function