Understanding Composition of Functions

In this class, We discuss Understanding Composition of Functions.

The reader should have prior knowledge of one-to-one and other functions. Click Here.

Composition of functions:

Let F: X -> Y and G: Y -> Z are two functions.

The composition G o F is given as G o F(x) = G(F(x)) for all x ∈ X.

The diagram below shows the functions F, G, and G o F

G(F(x1)) = G(y1) = z1.

G o F(x1) = z1

As above, find the values for all the x values.

Definition:

Let F: X -> Y and G: Y -> Z are two functions.

The composition relation G o F = {(x, z)| x ∈ X and z ∈ Z and ∃y (y ∈ Y and y = F(x) and z = G(y))} is called the composition of functions.

The composition of a function is also called a relative product of a function.