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


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.

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