One to One Function - Practice Questions & MCQ

A function f : X Y is called a one-one (or injective) function, if different elements of X have different images in B. i.e. no two elements of set X can have the same image. 

Consider,

f : X ⟶ Y, function given by y = f(x) = x , and 

X = {-2, 2, 4, 6} and Y = {-2, 2, 4, 6},  

Graphically it can be shown that for every x, there is a unique y (or no y has more than one x corresponding to it) as below and hence it is one-one.

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

f : X1 ⟶ X2

Method to check One-One Function

1. If x₁, x₂ X, then f(x₁) = f(x₂) ⇒ x₁ = x₂

2. A function is one - one iff no line parallel to X-axis meets the graph of function at more than one point.

3. Even degree polynomials are NOT one-one functions

Number of One - One Function

If A and B are finite sets having element m and n respectively, then the number of one-one function from A to B is