Into Function and Bijective function - Practice Questions & MCQ

Into Function:

A function f : X Y is said to be an into function if there exists an element in Y having no pre-image in A. 

In other words, if f : X Y is not onto mapping then it is an into mapping. 

Eg

As the element y₂ in codomain does not have a pre-image in domain, so it is into function

NOtE: If a function is not onto, then it is into and

If a function is not into, then it is onto.

Bijective Function

A function f : X Y is said to be bijective, if f is both one-one and onto (meaning it is both injective and surjective) 

Consider, X₁ = {1,2,3} and X₂ = {x,y,z}  

Eg

f : X₁ ⟶ X₂

The number of bijective function: 

If f(x) is bijective, and the function is from a finite set A to a finite set B, then 

And, the number of Bijective functions= m!

Equal Functions  

The two functions f and g are said to be equal if

• Domain(f) = Domain(g)
• Co-domain(f) = Co-domain(g), and
• f(x)=g(x) for all x belonging to domain