Composition of Functions

If there are two functions: f(x) and g(x), and the 2nd domain is within the range of the 1st, it can be defined as a new function that associates each element of the domain of f(x) with the value of g[f(x)].

Composition of Functions

(g o f) (x) = g [f(x)] = g (2x) = 3 (2x) +1 = 6x + 1

(g o f) (1) = 6 · 1 + 1 = 7

Domain

D(g o f) = {x pertenece Df / f(x) pertenece Dg}

Properties

Associative:

f o (g o h) = (f o g) o h

Not commutative.

f o g ≠ g o f

The identity element is the identity function, i(x) = x.

f o i = i o f = f


Examples

Function Exercise

Function Operations

Function Operations

Function Operations

Function Solution


Function Exercise

Function Operations

Function Solution


Function Exercise

Function Operations

Function Solution