Composition of Functions Examples 1

In this class, We discuss the Composition of Functions Examples 1.

The reader should have prior knowledge of the composition of functions. Click Here.

Example 1:

The set X = {1, 2, 3}

f, g, h are functions from X -> X, and their mapping is below.

f = {(1,2), (2, 3), (3, 1)}

g ={(1, 2), (2, 1), (3, 3)}

h = {(1, 1), (2, 2), (3,1)}

Find fog, gof, and fohog.

Solution:

fog = f(g(x)) = {(1, 3), (2, 2), (3, 1)}

gof = g(f(x)) = {(1, 1), (2, 3), (3, 2)}

fohog = f(h(g(x))) = {(1, 3), (2, 2), (3, 2)}

Example 2:

Let X = {1, 2, 3, 4}

f = {(1, 2), (2, 3), (3, 4), (4, 1)}

Find f^2 and f^3

Solution:

fof = f^2 = f(f(x)) = {(1, 3), (2, 4), (3, 1), (4, 2)}

fofof = f^3 = f(f(f(x))) = {(1, 4), (2, 1), (3, 2), (4, 3)}