Composite Functions | Assignment

Running head : COMPOSITE FUNCTIONS
COMPOSITE FUNCTIONS
Name of Student
Institution Affiliation

COMPOSITE FUNCTIONS
2
Reflect on the concept of composite and inverse functions
Composite function
Let f : A B and g: B C to be two functions . The function f takes an element x ∈A to an
element f(x) = y∈B and y is further taken by g to an element Z ∈C Therefore Z=g(y) = g of n
then for each x∈A a unique element Z=g(f(x)) of C (Cao, 2011) . This rule is therefore a
function of f and g ́ . Then if f:A B and g: B C be any two function then the composite
function of f of g is denoted by g of f and it is a function of g of A C is defined by ( g of
) ( x) = g(f(x)) ∀ x ∈ A
Inverse function
Let f be a 1-1 function from A onto B. Therefore ∀ yεB there exist x∈A such that f (x) = y and
since y is a 1-1 function (Shapiro, 2012). We can define a function say g from B onto A such that
g(y) = x. This function g is therefore called inverse function of f and denoted by function f-1.
What are the simplest composite and inverse functions you can imagine?
Example of composite function
Given f(x) = x2 + 6 and g(x) = 2x – 1, find
(f ο g)(x)
(f ο g)(x)
= f(2x – 1)
= (2x – 1)2 + 6
= 4x2 – 4x + 1 + 6
= 4x2 – 4x + 7
Inverse composite functions